@techreport{Boisvert1996:Eng,
address = {Gaithersburg, MD},
author = {Boisvert, Ronald F. and Pozo, Roldan and Remington, Karin A.},
file = {:D\:/Mendeley/Boisvert, Pozo, Remington - 1996 - The Matrix Market Exchange Formats Initial Design.pdf:pdf},
institution = {NISTIR 5935. National Institute of Standards and Technology},
pages = {14},
title = {{The Matrix Market Exchange Formats: Initial Design}},
url = {https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nistir5935.pdf},
year = {1996}
}
@book{Censor1997:Eng,
address = {New York},
author = {Censor, Yair and Zenios, Stavros A.},
file = {:D\:/Mendeley/Censor, Zenios - 1997 - Parallel Optimization Theory, Algorithms, and Applications.pdf:pdf},
publisher = {Oxford University Press},
title = {{Parallel Optimization: Theory, Algorithms, and Applications}},
year = {1997}
}
@article{Karmarkar1984:Eng,
abstract = {We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ellipsoid algorithm by a factor of O(n$\sim$'$\sim$). We prove that given a polytope P and a strictly in- terior point a E P, there is a projective transformation of the space that maps P, a to P', a' having the following property. The ratio of the radius of the smallest sphere with center a', containing P' to the radius of the largest sphere with center a' contained in P' is O(n). The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in poly- nomial time.},
author = {Karmarkar, N.},
doi = {10.1007/BF02579150},
file = {:D\:/Mendeley/Karmarkar - 1984 - A new polynomial-time algorithm for linear programming.pdf:pdf},
isbn = {0897911334},
issn = {02099683},
journal = {Combinatorica},
number = {4},
pages = {373--395},
title = {{A new polynomial-time algorithm for linear programming}},
volume = {4},
year = {1984}
}
@article{Malek2005:Eng,
abstract = {In this paper we represent two new methods for the solution of canonical form linear programming problems. In order to solve this linear programming problem we must minimize energy function of the corresponding neural network. Here energy function is considered as a Liapunov function and we use treated Hopfield neural network. First new method finds optimal solution for primal problem, using neural network, while second new method composes primal and dual problem and therefore finds optimal solution for both problems. Numerical results compared with simplex solution, and find that the convergence of two new methods to the correct solution is too fast, even faster than Neguyen's method. The new methods are fully stable.},
author = {Malek, A. and Yari, A.},
doi = {10.1016/J.AMC.2004.06.081},
file = {:D\:/Mendeley//Malek, Yari - 2005 - Primal-dual solution for the linear programming problems using neural networks.pdf:pdf},
issn = {0096-3003},
journal = {Applied Mathematics and Computation},
keywords = {Dynamical systems,Linear programming,Neural networks,Primal-dual problems},
number = {1},
pages = {198--211},
publisher = {Elsevier},
title = {{Primal-dual solution for the linear programming problems using neural networks}},
volume = {167},
year = {2005}
}
@inproceedings{Raina2009:Eng,
abstract = {The promise of unsupervised learning methods lies in their potential to use vast amounts of unlabeled data to learn complex, highly nonlinear models with millions of free parameters. We consider two well-known unsupervised learning models, deep belief networks (DBNs) and sparse coding, that have recentlybeen applied to a flurry of machine learning applications (Hinton & Salakhutdinov, 2006; Raina et al., 2007). Unfortunately, current learning algorithms for both models are too slow for large-scale applications, forcing researchers to focus on smaller-scale models, or to use fewer training examples. In this paper, we suggest massively parallel methods to help resolve these problems. We argue that modern graphics processors far surpass the computational capabilities of multicore CPUs, and have the potential to revolutionize the applicability of deep unsupervised learning methods. We develop general principles for massively parallelizing unsupervised learning tasks using graphics processors. We show that these principles can be applied to successfully scaling up learning algorithms for both DBNs and sparse coding. Our implementation of DBN learning is up to 70 times faster than a dual-core CPU implementation for large models. For example, we are able to reduce the time required to learn a four-layer DBN with 100 million free parameters from several weeks to around a single day. For sparse coding, we develop a simple, inherently parallel algorithm, that leads to a 5 to 15-fold speedup over previous methods. Copyright 2009.},
address = {New York, NY, USA},
author = {Raina, Rajat and Madhavan, Anand and Ng, Andrew Y.},
booktitle = {Proceedings of the 26th Annual International Conference on Machine Learning (ICML '09)},
doi = {10.1145/1553374.1553486},
file = {:D\:/Mendeley/Raina, Madhavan, Ng - 2009 - Large-scale deep unsupervised learning using graphics processors.pdf:pdf},
isbn = {9781605585161},
pages = {873--880},
publisher = {ACM Press},
title = {{Large-scale deep unsupervised learning using graphics processors}},
year = {2009}
}
@article{Fleming2021:Eng,
abstract = {Eco-driving assistance systems incorporating predictive or feedforward information are a promising technique to increase energy-efficiency and reduce (Formula presented.) emissions from road transportation. This work gives details of such a system that was recently developed by the authors, which uses real-time data from GPS and automotive radar to perform a predictive optimisation of a vehicle's speed profile and coaches a driver into fuel-saving and (Formula presented.) -reducing behaviour. A repeated-measures study carried out in a fixed-base driving simulator indicated an overall reduction in fuel consumption of 6.09\%, which was significantly greater than improvements expected from reductions in average speed. Adjusted for average speed, fuel-efficiency improvements when using the system are similar to those observed in unassisted eco-driving, but with improvements in travel time in motorway situations. Finally, an on-road prototype is described in which the optimisation is solved using data from vehicle sensors, successfully demonstrating that real-time implementation of the system is feasible.},
author = {Fleming, James and Yan, Xingda and Allison, Craig and Stanton, Neville and Lot, Roberto},
doi = {10.1049/ITR2.12047},
file = {:D\:/Mendeley/Fleming et al. - 2021 - Real-time predictive eco-driving assistance considering road geometry and long-range radar measurements.pdf:pdf},
issn = {1751-9578},
journal = {IET Intelligent Transport Systems},
number = {4},
pages = {573--583},
title = {{Real-time predictive eco-driving assistance considering road geometry and long-range radar measurements}},
volume = {15},
year = {2021}
}
@incollection{Sokolinskaya2018:Eng,
abstract = {This article presents a new iterative method for finding an approximate solution of a linear inequality system. This method uses the notion of pseudoprojection which is a generalization of the operation of projecting a point onto a closed convex set in Euclidean space. Pseudoprojecting is an iterative process based on Fejer approximations. The proposed pseudoprojection method is amenable to parallel implementation exploiting the subvector method, which is also presented in this article. We prove both the subvector method correctness and the convergence of the pseudoprojection method.},
address = {Cham, Switzerland},
author = {Sokolinskaya, Irina M.},
booktitle = {Parallel Computational Technologies. PCT 2018. Communications in Computer and Information Science, vol. 910},
doi = {10.1007/978-3-319-99673-8_16},
editor = {Sokolinsky, Leonid and Zymbler, Mikhail},
file = {:D\:/Mendeley/Sokolinskaya - 2018 - Parallel Method of Pseudoprojection for Linear Inequalities.pdf:pdf},
keywords = {Convergence,Fejer approximations,Iterative method,Linear inequality system,Parallel algorithm,Pseudoprojection},
pages = {216--231},
publisher = {Springer},
title = {{Parallel Method of Pseudoprojection for Linear Inequalities}},
year = {2018}
}
@inproceedings{Sokolinsky2020b,
abstract = {В статье рассматривается параллельный итерационный алгоритм проекционного типа для решения нестационарных систем линейных неравенств. Под нестационарной системой понимается сверхбольшая система неравенств, в которой коэффициенты при переменных и свободные члены могут меняться в процессе вычислений. Предложенный параллельный алгоритм использует понятие псевдопроекции, являющееся обобщением операции проектирования точки на гиперплоскость. Параллельная реализация алгоритма псевдопроекций выполнена на базе параллельного BSF-каркаса. На основе стоимостной метрики модели BSF получена аналитическая оценка границы масштабируемости алгоритма. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе, подтверждающие эффективность предложенного подхода.},
address = {Челябинск},
author = {Соколинский, Л. Б. and Соколинская, И. М.},
booktitle = {Параллельные вычислительные технологии – XIV международная конференция, ПаВТ'2020, г. Пермь, 31 марта–2 апреля 2020 г. Короткие статьи и описания плакатов},
doi = {10.14529/pct2020},
file = {:D\:/Mendeley/Соколинский, Соколинская - 2020 - Параллельный алгоритм решения нестационарных систем линейных неравенств.pdf:pdf},
keywords = {вычислительные системы,задача совместности,итерационный метод,кластерные,нестационарная система линейных неравенств,параллельный алгоритм,приближенное решение},
language = {russian},
pages = {275--286},
publisher = {Издательский центр ЮУрГУ},
title = {{Параллельный алгоритм решения нестационарных систем линейных неравенств}},
url = {http://omega.sp.susu.ru/pavt2020/short/098.pdf},
year = {2020}
}
@inproceedings{Dolganina2022:Eng,
abstract = {Currently, South Ural State University (SUSU) has significant achievements in supercomputer modeling, artificial intelligence and Big Data. The high-performance resources of SUSU include an energy-efficient supercomputer “Tornado SUSU” and a specialized multiprocessor complex “Neurocomputer”. The “Tornado SUSU” supercomputer and the “Neurocomputer” complex are at the center of the scientific life of the University and enable complex calculations for engineering, natural and human sciences, artificial intelligence. The high-performance resources of SUSU are used in education and for calculating the tasks of the University's partners. The paper describes the “Tornado SUSU” supercomputer and “Neurocomputer” complex technical features, system and application parallel software, scientific and engineering tasks solved with the help of the SUSU resources.},
address = {City: Cham},
author = {Dolganina, Natalya and Ivanova, Elena and Bilenko, Roman and Rekachinsky, Alexander},
booktitle = {Parallel Computational Technologies. PCT 2022. Communications in Computer and Information Science, vol. 1618},
doi = {10.1007/978-3-031-11623-0_4},
editor = {Sokolinsky, L. and Zymbler, M.},
file = {:D\:/Mendeley/Dolganina et al. - 2022 - HPC Resources of South Ural State University.pdf:pdf},
isbn = {9783031116223},
issn = {18650937},
keywords = {Neural networks,Neurocomputer,Parallel storage system,Supercomputer,Supercomputer administration,Supercomputer modeling},
pages = {43--55},
publisher = {Springer},
title = {{HPC Resources of South Ural State University}},
year = {2022}
}
@inproceedings{Sokolinskaya2016,
address = {Москва},
author = {Соколинская, И.М. and Соколинский, Л.Б.},
booktitle = {Суперкомпьютерные дни в России: труды международной конференции (26-27 сентября 2016 г., г. Москва)},
language = {russian},
pages = {294--306},
publisher = {Изд-во МГУ},
title = {{Модифицированный следящий алгоритм для решения нестационарных задач линейного программирования на кластерных вычислительных системах с многоядерными ускорителями}},
url = {https://2016.russianscdays.org/files/pdf16/294.pdf},
year = {2016}
}
@article{Sokolinsky2021d,
abstract = {В статье представлен параллельный алгоритм валидации решений задач линейного программирования. Идея метода состоит в том, чтобы генерировать регулярный набор точек на гиперсфере малого радиуса, центрированной в точке тестируемого решения. Целевая функция вычисляется для каждой точки валидационного множества, принадлежащей допустимой области. Если все полученные значения меньше или равны значению целевой функции в точке, проверяемой как решение, то эта точка считается корректным решением. Параллельная реализация алгоритма VaLiPro выполнена на языке C++ с использованием параллельного BSF-каркаса, инкапсулирующего в проблемно-независимой части своего кода все аспекты, связанные с распараллеливанием программы на базе библиотеки MPI. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе, подтверждающие эффективность предложенного подхода.},
author = {Соколинский, Леонид Борисович and Соколинская, Ирина Михайловна},
doi = {10.26089/NUMMET.V22R416},
file = {:D\:/Mendeley/Соколинский, Соколинская - 2021 - О валидации решений задач линейного программирования на кластерных вычислительных системах.pdf:pdf},
issn = {1726-3522},
journal = {Вычислительные методы и программирование},
keywords = {VaLiPro,валидатор решений,кластерные вычислительные системы,линейное программирование,параллельный BSF каркас,параллельный алгоритм},
language = {russian},
number = {4},
pages = {252--261},
title = {{О валидации решений задач линейного программирования на кластерных вычислительных системах}},
url = {https://num-meth.ru/index.php/journal/article/view/1175},
volume = {22},
year = {2021}
}
@incollection{Tolla2014:Eng,
abstract = {The simplex method allows to solve a good number of linear programs with up to about 50,000 variables. Joseph Fourier proposed methods for solving systems of linear inequalities and a minimization method of ||A. x ‐ b||8 that had many points in common with the method invented by Dantzig. Since the creation of the first interior algorithm, many programs have been created; they include procedures for taking into account bound constraints, procedures for pre‐optimization, for sensitivity analysis and for parametrization, already present in simplistic programs. They often use the principles of primal, dual and primal–dual algorithms. Interior methods are used to solve combinatorial optimization problems of great size. Furthermore, they have been generalized to the solution of nonlinear programs and to semi‐definite optimization.},
address = {Hoboken, NJ, USA},
author = {Tolla, P.},
booktitle = {Concepts of Combinatorial Optimization},
chapter = {7},
doi = {10.1002/9781119005216.ch7},
edition = {2},
editor = {Paschos, Vangelis Th.},
file = {:D\:/Mendeley/Tolla - 2014 - A Survey of Some Linear Programming Methods.pdf:pdf},
keywords = {Dantzig simplex method,interior methods,linear programming methods},
pages = {157--188},
publisher = {John Wiley and Sons},
title = {{A Survey of Some Linear Programming Methods}},
year = {2014}
}
@article{Demin2017:Eng,
author = {Demin, Dmitriy A.},
doi = {10.15587/1729-4061.2017.105294},
file = {:D\:/Mendeley/Demin - 2017 - Synthesis of optimal control of technological processes based on a multialternative parametric description of the final s.pdf:pdf},
issn = {1729-3774},
journal = {Eastern-European Journal of Enterprise Technologies},
number = {4(87)},
pages = {51--63},
title = {{Synthesis of optimal control of technological processes based on a multialternative parametric description of the final state}},
volume = {3},
year = {2017}
}
@incollection{Polyak2005,
abstract = {Предлагается случайный субградиентный метод решения общей задачи совместности выпуклых неравенств с большим (или бесконечным) числом неравенств. При условии строгой разрешимости метод сходится к решению за конечное число шагов с вероятностью единица. Также предлагается сходящаяся версия метода для случая несовместной системы. Алгоритм может применяться к решению линейных матричных неравенств, возникающих в задачах теории управления. Численное моделирование показывает высокую эффективность метода для задач большой размерности.},
address = {СПб.},
author = {Поляк, Борис Теодорович},
booktitle = {Стохастическая оптимизация в информатике},
editor = {Граничин, О. Н.},
file = {:D\:/Mendeley/Поляк - 2005 - Рандомизированные алгоритмы решения выпуклых неравенств.pdf:pdf},
isbn = {5-288-03700-0},
language = {russian},
pages = {123--127},
publisher = {Издательство С.-Петербургского университета},
title = {{Рандомизированные алгоритмы решения выпуклых неравенств}},
url = {https://www.math.spbu.ru/user/gran/sb1/polyak.pdf},
year = {2005}
}
@article{Eremin1968:Eng,
author = {Eremin, I. I.},
doi = {10.1007/BF01094336},
file = {:D\:/Mendeley/Eremin - 1968 - Methods of Fejer's approximations in convex programming.pdf:pdf},
issn = {0001-4346},
journal = {Mathematical Notes of the Academy of Sciences of the USSR},
keywords = {Fejer's approximations,convex programming},
number = {2},
pages = {139--149},
publisher = {Kluwer Academic Publishers - Plenum Publishers},
title = {{Methods of Fejer's approximations in convex programming}},
url = {http://link.springer.com/10.1007/BF01094336},
volume = {3},
year = {1968}
}
@inproceedings{Schlenkrich2023:Eng,
abstract = {Production scheduling is challenging and the body of literature addressing various variants of the problem is large. It can roughly be divided into two streams: The first stream addresses and generalizes established scheduling problems, being general in the sense that they are not only applicable in a particular industry. The second stream works on less generic scheduling approaches for real industry cases by enriching standard models with all the required realistic aspects, such as process overlapping or sequence dependent setup times. Furthermore, different approaches have different limitations in terms of the problem size that they can tackle. The rise of Industry 4.0 has lead to a significant increase in data collection activities and the gathered information is used to build larger and more complex models. Industrial use cases may consist of several thousand operations on a large variety of machines, while classical benchmark instances tend to range up to only a few hundred of operations. It is therefore necessary to identify and highlight approaches, that can meet the challenges of scheduling in the era of Industry 4.0 and are suitable to tackle large scale problems. In this work, we conduct a structured literature review on scheduling problems incorporating several real world aspects among a broad range of use cases. Based on the identified publications we find that advanced solution approaches for large scale scheduling problems usually belong to one out of three categories, namely metaheuristic methods, constraint programming and machine learning. Our review shows that comparably few contributions tackling (very) large scale problems exist, emphasizing the need for additional research in this field. We identify promising approaches for further research, such as powerful metaheuristics combining concepts of tabu search and genetic algorithms. We further discuss the possibility to enhance solution methods by integrating constraint programming concepts and investigating problem decomposition.},
author = {Schlenkrich, Manuel and Parragh, Sophie N.},
booktitle = {4th International Conference on Industry 4.0 and Smart Manufacturing. Procedia Computer Science},
doi = {10.1016/J.PROCS.2022.12.301},
editor = {Longo, Francesco and Affenzeller, Michael and Padovano, Antonio and Shen, Weiming},
file = {:D\:/Mendeley/Schlenkrich, Parragh - 2023 - Solving large scale industrial production scheduling problems with complex constraints an overview of the.pdf:pdf},
issn = {1877-0509},
keywords = {Industry 4.0,Large scale scheduling,complex constraints,literature review},
pages = {1028--1037},
publisher = {Elsevier},
title = {{Solving large scale industrial production scheduling problems with complex constraints: an overview of the state-of-the-art}},
volume = {217},
year = {2023}
}
@inproceedings{Scholl2019:Eng,
abstract = {To enhance the temperature dependent aspects -efficiency, safety and aging-of battery electric vehicles an innovative thermal management system is developed. The system focuses on distributing, storing and releasing heat to support the warm up process of the battery at low ambient temperatures. Additionally, cooling the power train components at high ambient temperatures is intended. In order to increase the system's efficiency, a rule-based operational strategy is developed. This strategy is optimized using Particle Swarm optimization with an objective function which is specifically created for that problem. The function evaluates the performance of the system by considering its thermal effect, the costs for the user and the energy demand. The effect of the system and the benefit of an optimized operational strategy are demonstrated by results from simulations of the WLTP with a small battery electric vehicle (Renault Twizy).},
author = {Scholl, Manuel and Minnerup, Katharina and Reiter, Christoph and Bernhardt, Benno and Weisbrodt, Elena and Newiger, Sebastian},
booktitle = {14th International Conference on Ecological Vehicles and Renewable Energies, EVER 2019},
doi = {10.1109/EVER.2019.8813657},
file = {:D\:/Mendeley/Scholl et al. - 2019 - Optimization of a thermal management system for battery electric vehicles.pdf:pdf},
isbn = {9781728137032},
keywords = {Electric vehicles,Operational strategy,Optimization,PSO,Thermal management},
publisher = {IEEE},
title = {{Optimization of a thermal management system for battery electric vehicles}},
year = {2019}
}
@article{Sokolinsky2021:Eng,
abstract = {В статье рассматривается новая модель параллельных вычислений под названием Bulk Synchronous Farm (BSF), которая фокусируется на оценке масштабируемости итерационных алгоритмов с интенсивными вычислениями, ориентированных на кластерные вычислительные системы. Основным преимуществом предложенной модели является то, что она позволяет оценить масштабируемость параллельного алгоритма еще до его реализации. Еще одной важной особенностью модели BSF является представление исходных данных в виде списков, что значительно упрощает логику построения приложений. В модели BSF компьютер представляет собой набор процессорных узлов, соединенных сетью и организованных в соответствии с парадигмой master/slave. Представлена стоимостная метрика модели BSF. Эта метрика требует, чтобы алгоритм был представлен в виде операций над списками. Это позволяет вывести формулу, предсказывающую границу масштабируемости параллельной программы: максимальное число процессорных узлов, после которого ускорение начинает уменьшаться. В статье приведены примеры применения модели BSF для проектирования и анализа параллельных численных алгоритмов. Масштабные вычислительные эксперименты, проведенные на кластерной вычислительной системе, подтверждают адекватность аналитических оценок, полученных с использованием модели BSF.},
author = {Sokolinsky, Leonid B.},
doi = {10.1016/j.jpdc.2020.12.009},
file = {:D\:/Mendeley/Sokolinsky - 2021 - BSF A parallel computation model for scalability estimation of iterative numerical algorithms on cluster computing s.pdf:pdf},
issn = {07437315},
journal = {Journal of Parallel and Distributed Computing},
keywords = {BSF model,Bulk synchronous farm,Cluster computing systems,Iterative numerical algorithms,Parallel computation model},
pages = {193--206},
title = {{BSF: A parallel computation model for scalability estimation of iterative numerical algorithms on cluster computing systems}},
volume = {149},
year = {2021}
}
@article{Sokolinsky2021a:Eng,
abstract = {The BSF-skeleton is designed for creating parallel programs in C++ using the MPI library. The scope of the BSF-skeleton is cluster computing systems and iterative numerical algorithms of high computational complexity. The BSF-skeleton completely encapsulates all aspects that are associated with parallelizing a program on a cluster computing system. The source code of the BSF-skeleton is freely available on Github at https://github.com/leonid-sokolinsky/BSF-skeleton.},
author = {Sokolinsky, Leonid B.},
doi = {10.1016/j.mex.2021.101437},
file = {:D\:/Mendeley//Sokolinsky - 2021 - BSF-skeleton A Template for Parallelization of Iterative Numerical Algorithms on Cluster Computing Systems.pdf:pdf},
issn = {2215-0161},
journal = {MethodsX},
keywords = {BSF-skeleton,C++,MPI,parallel programming},
pages = {Article number 101437},
title = {{BSF-skeleton: A Template for Parallelization of Iterative Numerical Algorithms on Cluster Computing Systems}},
volume = {8},
year = {2021}
}
@article{Hall2010:Eng,
abstract = {The simplex method is frequently the most efficient method of solving linear programming (LP) problems. This paper reviews previous attempts to parallelise the simplex method in relation to efficient serial simplex techniques and the nature of practical LP problems. For the major challenge of solving general large sparse LP problems, there has been no parallelisation of the simplex method that offers significantly improved performance over a good serial implementation. However, there has been some success in developing parallel solvers for LPs that are dense or have particular structural properties. As an outcome of the review, this paper identifies scope for future work towards the goal of developing parallel implementations of the simplex method that are of practical value.},
author = {Hall, J.A.J.},
doi = {10.1007/s10287-008-0080-5},
file = {:D\:/Mendeley/Hall - 2010 - Towards a practical parallelisation of the simplex method.pdf:pdf},
issn = {1619697X},
journal = {Computational Management Science},
keywords = {Linear programming,Parallel computing,Simplex method,Sparse},
number = {2},
pages = {139--170},
publisher = {Springer},
title = {{Towards a practical parallelisation of the simplex method}},
volume = {7},
year = {2010}
}
@article{Zak1995:Eng,
abstract = {In this paper we study three different classes of neural network models for solving linear programming problems. We investigate the following characteristics of each model: model complexity, complexity of individual neurons, and accuracy of solutions. Simulation examples are given to illustrate the dynamical behavior of each model.},
author = {Zak, S. H. and Upatising, V.},
doi = {10.1109/72.363446},
file = {:D\:/Mendeley/Zak, Upatising - 1995 - Solving Linear Programming Problems with Neural Networks A Comparative Study(2).pdf:pdf},
issn = {19410093},
journal = {IEEE Transactions on Neural Networks},
number = {1},
pages = {94--104},
title = {{Solving Linear Programming Problems with Neural Networks: A Comparative Study}},
volume = {6},
year = {1995}
}
@article{Deng2021:Eng,
abstract = {In the last decade, High-Frequency Trading (HFT) has become a popular issue in the futures market, which has attracted much attention from numerous researchers. In this study, an intelligent decision support system is proposed for apple futures high-frequency trading. First, three eXtreme Gradient Boosting (XGBoost) based models use the feature inputs from multiple time scales for return and direction prediction. Then, based on a pre-designed trading rule, the signals of long and short-selling are determined, and corresponding transactions are executed. In order to retain considerable profits in time and to avoid serious losses possibly caused by sudden and huge price changes toward the opposite direction as predictions, a position closing function is implemented in the trading rule. Meanwhile, Particle Swarm Optimization (PSO) is employed to optimize the parameters of the trading rule as well as the XGBoost parameters. By evaluating the experimental results, we observed that the proposed approach successfully achieved the best performance in terms of direction prediction accuracy, transaction returns, as well as return/risk ratio. It could be inferred from the experimental results that the proposed approach could provide decision support and beneficial reference for market traders involved in high-frequency trading of the apple futures.},
author = {Deng, Shangkun and Huang, Xiaoru and Wang, Jiahui and Qin, Zhaohui and Fu, Zhe and Wang, Aiming and Yang, Tianxiang},
doi = {10.1109/ACCESS.2020.3047138},
file = {:D\:/Mendeley/Deng et al. - 2021 - A Decision Support System for Trading in Apple Futures Market Using Predictions Fusion.pdf:pdf},
issn = {21693536},
journal = {IEEE Access},
keywords = {Futures market,multiple time scale,parameters optimization,trading rule},
pages = {1271--1285},
publisher = {IEEE},
title = {{A Decision Support System for Trading in Apple Futures Market Using Predictions Fusion}},
volume = {9},
year = {2021}
}
@article{Liu2016:Eng,
abstract = {In this paper, a one-layer recurrent network is proposed for solving a non-smooth convex optimization subject to linear inequality constraints. Compared with the existing neural networks for optimization, the proposed neural network is capable of solving more general convex optimization with linear inequality constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds.},
author = {Liu, X. and Zhou, M.},
doi = {10.1016/j.chaos.2016.03.009},
file = {:D\:/Mendeley/Liu, Zhou - 2016 - A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints.pdf:pdf},
issn = {09600779},
journal = {Chaos, Solitons and Fractals},
keywords = {Finite-time convergence,Linear inequality constraints,Lower bounds,Neural network,Non-smooth analysis},
pages = {39--46},
publisher = {Elsevier Ltd},
title = {{A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints}},
volume = {87},
year = {2016}
}
@misc{Gay2013:Eng,
author = {Gay, David M.},
keywords = {NETLIB-LP},
title = {{Netlib-Lp Linear Programming problems}},
url = {http://www.netlib.org/lp/},
urldate = {2022-02-15},
year = {2013}
}
@incollection{Meisel2011:Eng,
abstract = {Vehicle routing is one of the major tasks in the context of transportation. The predominant influences currently inducing a change in transportation operations are outlined in Chap. 1. In particular these influences lead to an increased economic relevance of dynamic...},
address = {New York, NY},
author = {Meisel, Stephan},
booktitle = {Anticipatory Optimization for Dynamic Decision Making. Operations Research/Computer Science Interfaces Series, vol. 51},
doi = {10.1007/978-1-4614-0505-4_6},
isbn = {978-1-4614-0505-4},
pages = {77--96},
publisher = {Springer},
title = {{Dynamic Vehicle Routing}},
year = {2011}
}
@incollection{Branke2002:Eng,
abstract = {Whenever a change in a dynamic optimization problem occurs i.e. when the optimization goal, the problem instance, or some restrictions change, the optimum to that problem might change as well. If this is the case, an adaptation of the old solution is necessary.},
address = {Boston, MA},
author = {Branke, J{\"{u}}rgen},
booktitle = {Evolutionary Optimization in Dynamic Environments. Genetic Algorithms and Evolutionary Computation, vol. 3},
doi = {10.1007/978-1-4615-0911-0_2},
file = {:D\:/Mendeley/Branke - 2002 - Optimization in Dynamic Environments.pdf:pdf},
isbn = {978-1-4613-5300-3},
pages = {13--29},
publisher = {Springer},
title = {{Optimization in Dynamic Environments}},
year = {2002}
}
@article{Hall2005:Eng,
abstract = {The revised simplex method is often the method of choice when solving large scale sparse linear programming problems, particularly when a family of closely-related problems is to be solved. Each iteration of the revised simplex method requires the solution of two linear systems and a matrix vector product. For a significant number of practical problems the result of one or more of these operations is usually sparse, a property we call hyper-sparsity. Analysis of the commonly-used techniques for implementing each step of the revised simplex method shows them to be inefficient when hyper-sparsity is present. Techniques to exploit hyper-sparsity are developed and their performance is compared with the standard techniques. For the subset of our test problems that exhibits hyper-sparsity, the average speedup in solution time is 5.2 when these techniques are used. For this problem set our implementation of the revised simplex method which exploits hyper-sparsity is shown to be competitive with the leading commercial solver and significantly faster than the leading public-domain solver.},
author = {Hall, J.A.J. and McKinnon, K.I.M.},
doi = {10.1007/s10589-005-4802-0},
file = {:D\:/Mendeley/Hall, McKinnon - 2005 - Hyper-sparsity in the revised simplex method and how to exploit it.pdf:pdf},
issn = {09266003},
journal = {Computational Optimization and Applications},
keywords = {Linear programming,Revised simplex method,Sparsity},
number = {3},
pages = {259--283},
publisher = {Springer},
title = {{Hyper-sparsity in the revised simplex method and how to exploit it}},
volume = {32},
year = {2005}
}
@article{Sodhi2005:Eng,
abstract = {Dynamic linear programming (LP) models for asset-liability management (ALM) are quite powerful and flexible but face two challenges: (1) many modeling choices, not all consistent with one another or with finance theory, and (2) solution difficulties due to the large number of scenarios obtained from standard interest-rate models. We first survey these modeling choices with a view to help researchers make self-consistent choices. Next, we review how the dynamic LP model for ALM and the representation of uncertainty therein have been simplified in the past to motivate new or hybrid models emphasizing tractability. To this end, we review existing static LP models as extreme modeling simplifications and aggregation as a simplification of uncertainty.},
author = {Sodhi, M. S.},
doi = {10.1287/opre.1040.0185},
file = {:D\:/Mendeley/Sodhi - 2005 - LP modeling for asset-liability management A survey of choices and simplifications.pdf:pdf},
isbn = {0030-364X},
issn = {0030-364X},
journal = {Operations Research},
keywords = {finance: portfolio,financial institutions: banks,i},
number = {2},
pages = {181--196},
title = {{LP modeling for asset-liability management: A survey of choices and simplifications}},
volume = {53},
year = {2005}
}
@book{Fathi2019:Eng,
address = {Cham, Switzerland},
doi = {10.1007/978-3-030-28565-4},
editor = {Fathi, Mahdi and Khakifirooz, Marzieh and Pardalos, Panos M.},
file = {:D\:/Mendeley/Unknown - 2019 - Optimization in Large Scale Problems Industry 4.0 and Society 5.0 Applications.pdf:pdf},
isbn = {978-3-030-28564-7},
pages = {XI, 340},
publisher = {Springer},
title = {{Optimization in Large Scale Problems: Industry 4.0 and Society 5.0 Applications}},
year = {2019}
}
@article{Gay1985:Eng,
author = {Gay, David M.},
file = {:D\:/Mendeley/Gay - 1985 - Electronic mail distribution of linear programming test problems.pdf:pdf},
journal = {Mathematical Programming Society COAL Bulletin},
keywords = {NETLIB-LP},
pages = {10--12},
title = {{Electronic mail distribution of linear programming test problems}},
volume = {13},
year = {1985}
}
@article{LeCun2015:Eng,
abstract = {Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.},
author = {LeCun, Y. and Bengio, Y. and Hinton, G.},
doi = {10.1038/nature14539},
file = {:D\:/Mendeley/LeCun, Bengio, Hinton - 2015 - Deep learning.pdf:pdf},
journal = {Nature},
keywords = {CNN,convolutional neural network,deep learning,neural networks},
number = {7553},
pages = {436--444},
publisher = {Nature Publishing Group},
title = {{Deep learning}},
volume = {521},
year = {2015}
}
@article{Asadi2019:Eng,
abstract = {In this paper, we analyze a feasible predictor-corrector linear programming variant of Mehrotra's algorithm. The analysis is done in the negative infinity neighborhood of the central path. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The complexity result establishes an improvement of factor n 3 in the theoretical complexity of an earlier presented variant in [2], which is a huge improvement. We examine the performance of our algorithm by comparing its implementation results to solve some NETLIB problems with the algorithm presented in [2].},
author = {Asadi, Soodabeh and Mansouri, Hossein},
doi = {10.3934/naco.2019011},
file = {:D\:/Mendeley/Asadi, Mansouri - 2019 - A Mehrotra type predictor-corrector interior-point algorithm for linear programming.pdf:pdf},
issn = {21553297},
journal = {Numerical Algebra, Control and Optimization},
keywords = {Central path,Interior-point algorithm,Iteration complexity,Linear programming,Predictor-corrector},
number = {2},
pages = {147--156},
publisher = {American Institute of Mathematical Sciences},
title = {{A Mehrotra type predictor-corrector interior-point algorithm for linear programming}},
volume = {9},
year = {2019}
}
@article{Kaczmarz1993:Eng,
author = {Kaczmarz, Stefan},
doi = {10.1080/00207179308934446},
file = {:D\:/Mendeley/Kaczmarz - 1993 - Approximate solution of systems of linear equations.pdf:pdf},
issn = {0020-7179},
journal = {International Journal of Control},
number = {6},
pages = {1269--1271},
publisher = {Taylor & Francis Group},
title = {{Approximate solution of systems of linear equations}},
url = {https://www.tandfonline.com/doi/abs/10.1080/00207179308934446},
volume = {57},
year = {1993}
}
@article{Ansorge1984:Eng,
abstract = {Recently the method of Kaczmarz for the solution of linear equations became interesting again. This method converges always to a solution provided that at least one solution exists. Also the method of Cimmino converges (almost) always but shows some disadvantages. A modification of the Cimmino-method is presented which makes it as interesting as the Kaczmarzmethod. In certain cases, the new method is even faster.},
author = {Ansorge, R.},
doi = {10.1007/BF02242280},
file = {:D\:/Mendeley/Ansorge - 1984 - Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equa.pdf:pdf},
issn = {1436-5057},
journal = {Computing},
keywords = {Cimmino method,Kaczmarz method},
number = {3},
pages = {367--375},
publisher = {Springer},
title = {{Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations}},
volume = {33},
year = {1984}
}
@book{Roos2005:Eng,
abstract = {Linear Optimization (LO) is one of the most widely applied and taught techniques in mathematics, with applications in many areas of science, commerce and industry. The dramatically increased interest in the subject is due mainly to advances in computer technology and the development of Interior Point Methods (IPMs) for LO. This book provides a unified presentation of the field. The authors present a self-contained comprehensive interior point approach to both the theory of LO and algorithms for LO (design, convergence, complexity, asymptotic behaviour and computational issues). A common thread throughout the book is the role of strictly complementary solutions, which play a crucial role in the interior point approach and distinguishes the new approach from the classical Simplex-based approach. The approach to LO in this book is new in many aspects. In particular the IPM and self-dual model based development of duality theory is surprisingly elegant. The algorithmic part of this book contains a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis. The comprehensive coverage of the subject, together with the clarity of presentation, ensures that this book will be an invaluable resource for researchers and professionals who wish to develop their understanding of LO and IPMs. Numerous exercises are provided to help consolidate understanding of the material and more than 45 figures are included to illustrate the characteristics of the algorithms. A general understanding of linear algebra and calculus is assumed. The first chapters provide a self-contained introduction to LO for readers who are unfamiliar with LO methods; however these chapters are also of interest for others who want to have a fresh look at the topic. This book is intended for the optimization researcher community, advanced undergraduate and graduate students who are interested to learn the fundamentals and major variants of Interior Point Methods for linear optimization, who want to have a comprehensive introduction to Interior Point Methods that revolutionized the theory and practice of modern optimization.},
address = {New York},
author = {Roos, Cornelis and Terlaky, Tamas and Vial, Jean-Philippe},
doi = {10.1007/b100325},
file = {:D\:/Mendeley/Roos, Terlaky, Vial - 2005 - Interior Point Methods for Linear Optimization.pdf:pdf},
isbn = {0-387-26378-0},
keywords = {Interior point methods,Linear programming,Polynomial complexity,algorithms complexity,linear optimization},
pages = {500},
publisher = {Springer},
title = {{Interior Point Methods for Linear Optimization}},
year = {2005}
}
@inproceedings{Kazarinov2017:Eng,
abstract = {This article describes the automated control systems of steam boiler modes at the electric power plant applying the criterion of using the minimum natural gas amount. This system is based on the electric power station the steam boilers of which operate using a mixture of fuel gases with unstable characteristics and which generate steam for the entire steam supply line. In this system, one of the most significant aspects is the subsystem of the combustion rate control designed for sustaining the preset steam consumption rate at the boiler's exit. This subsystem is reviewed together with the steam pressure controller in the main steam pipe. The combustion rate controller operates basing upon the heat absorption efficiency impulse. This impulse represents a sum of steam consumption impulses from the boiler and the velocity of change in the boiler drum pressure. The signal output of the combustion rate controller impacts the control valve of natural gas. Studies have been conducted on combustion rate controllers at steam boilers of the electric power plant. These studies proved the controller's efficiency.},
author = {Kazarinov, L. S. and Shnayder, D. A. and Kolesnikova, O. V.},
booktitle = {2017 International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2017 - Proceedings},
doi = {10.1109/ICIEAM.2017.8076177},
file = {:D\:/Mendeley/Kazarinov, Shnayder, Kolesnikova - 2017 - Heat load control in steam boilers.pdf:pdf},
isbn = {9781509056484},
keywords = {energy efficiency,heat load control,steam boiler,thermal power plant},
publisher = {IEEE},
title = {{Heat load control in steam boilers}},
year = {2017}
}
@article{Sun2016:Eng,
author = {Sun, Jie and Meng, Fanwen and Dang, Yazheng},
doi = {10.3934/naco.2016023},
file = {:D\:/Mendeley/Sun, Meng, Dang - 2016 - Convergence analysis of a parallel projection algorithm for solving convex feasibility problems.pdf:pdf},
issn = {2155-3289},
journal = {Numerical Algebra, Control and Optimization},
number = {4},
pages = {505--519},
title = {{Convergence analysis of a parallel projection algorithm for solving convex feasibility problems}},
volume = {6},
year = {2016}
}
@article{Gondzio2014:Eng,
abstract = {Impossibility of finding local realistic models for quantum correlations due to entangle- ment is an important fact in foundations of quantum physics, gaining now new applica- tions in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher- level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with an innovative matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve substantially larger problems. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is in- tended for all audiences, no quantum-mechanical background is necessary.},
author = {Gondzio, J. and Gruca, J. A. and Hall, J. A. J. and Laskowski, W. and Zukowski, M.},
doi = {10.1016/j.cam.2013.12.003},
file = {:D\:/Mendeley/Gondzio et al. - 2014 - Solving large-scale optimization problems related to Bell's Theorem.pdf:pdf},
issn = {03770427},
journal = {Journal of Computational and Applied Mathematics},
keywords = {Interior point methods,Large-scale optimization,Matrix-free methods,Quantum information},
pages = {392--404},
title = {{Solving large-scale optimization problems related to Bell's Theorem}},
volume = {263},
year = {2014}
}
@article{Censor1982:Eng,
abstract = {The iterative method of Cimmino for solving linear equations is generalized to linear inequalities. We also present a Richardson-type iterative method for solving the inequality problem, which includes the generalized Cimmino scheme. Convergence proofs are provided.},
author = {Censor, Yair and Elfving, Tommy},
doi = {10.1016/0024-3795(82)90149-5},
file = {:D\:/Mendeley/Censor, Elfving - 1982 - New methods for linear inequalities.pdf:pdf},
issn = {00243795},
journal = {Linear Algebra and its Applications},
keywords = {Cimmino scheme,Richardson-type iterative method,convergence,iterative method,linear equations},
pages = {199--211},
publisher = {North-Holland},
title = {{New methods for linear inequalities}},
url = {http://www.sciencedirect.com/science/article/pii/0024379582901495 http://linkinghub.elsevier.com/retrieve/pii/0024379582901495},
volume = {42},
year = {1982}
}
@article{Ferrer2016:Eng,
abstract = {The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems.},
author = {Ferrer, A. and Goberna, M. A. and Gonzalez-Gutierrez, E. and Todorov, M. I.},
doi = {10.1007/S10479-016-2135-2},
file = {:D\:/Mendeley/Ferrer et al. - 2016 - A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem.pdf:pdf},
issn = {1572-9338},
journal = {Annals of Operations Research 2016 258:2},
keywords = {Combinatorics,Operations Research/Decision Theory,Relaxation method,Theory of Computation},
number = {2},
pages = {587--612},
title = {{A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem}},
volume = {258},
year = {2016}
}
@article{Gonzalez-Gutierrez2012:Eng,
abstract = {The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. We consider solving linear semi-infinite inequality systems via an extension of the relaxation method for finite linear inequality systems. The difficulties are discussed and a convergence result is derived under fairly general assumptions on a large class of linear semi-infinite inequality systems.},
author = {Gonzalez-Gutierrez, E. and Todorov, M. I.},
doi = {10.1007/s11590-010-0244-4},
file = {:D\:/Mendeley/Gonzalez-Gutierrez, Todorov - 2012 - A relaxation method for solving systems with infinitely many linear inequalities.pdf:pdf},
issn = {1862-4472},
journal = {Optimization Letters},
keywords = {linear inequality systems,relaxation method},
number = {2},
pages = {291--298},
publisher = {Springer-Verlag},
title = {{A relaxation method for solving systems with infinitely many linear inequalities}},
url = {http://link.springer.com/10.1007/s11590-010-0244-4},
volume = {6},
year = {2012}
}
@inproceedings{Chung2015:Eng,
abstract = {This paper is to discuss how to apply large-scale linear programming (LP) in business analytics. Two types of scenario-based LP problems are described, which would become very large-scale LP problems due to the availability of big data. Possible solution approaches are discussed according to the special structure of the problems. Further development of the solution methods is also included.},
author = {Chung, W.},
booktitle = {2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)},
doi = {10.1109/IEEM.2015.7385970},
file = {:D\:/Mendeley/Chung - 2015 - Applying large-scale linear programming in business analytics.pdf:pdf},
isbn = {9781467380669},
issn = {2157362X},
keywords = {CVaR,Decomposition methods,Large-scale LP},
pages = {1860--1864},
publisher = {IEEE},
title = {{Applying large-scale linear programming in business analytics}},
year = {2015}
}
@article{Koch2004:Eng,
abstract = {With standard linear programming solvers there is always some uncertainty about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the exact optimal objective values for all NETLIB problems.},
author = {Koch, Thorsten},
doi = {10.1016/S0167-6377(03)00094-4},
file = {:D\:/Mendeley/Koch - 2004 - The final NETLIB-LP results.pdf:pdf},
issn = {0167-6377},
journal = {Operations Research Letters},
keywords = {NETLIB-LP},
number = {2},
pages = {138--142},
title = {{The final NETLIB-LP results}},
volume = {32},
year = {2004}
}
@article{Brogaard2014:Eng,
abstract = {We examine the role of high-frequency traders (HFTs) in price discovery and price efficiency. Overall HFTs facilitate price efficiency by trading in the direction of permanent price changes and in the opposite direction of transitory pricing errors, both on average and on the highest volatility days. This is done through their liquidity demanding orders. In contrast, HFTs' liquidity supplying orders are adversely selected. The direction of HFTs' trading predicts price changes over short horizons measured in seconds. The direction of HFTs' trading is correlated with public information, such as macro news announcements, market-wide price movements, and limit order book imbalances.},
author = {Brogaard, J. and Hendershott, T. and Riordan, R.},
doi = {10.1093/rfs/hhu032},
file = {:D\:/Mendeley/Brogaard, Hendershott, Riordan - 2014 - High-Frequency Trading and Price Discovery.pdf:pdf},
issn = {0893-9454},
journal = {Review of Financial Studies},
keywords = {Algorithmic trading,High-frequency trading},
number = {8},
pages = {2267--2306},
title = {{High-Frequency Trading and Price Discovery}},
volume = {27},
year = {2014}
}
@article{Dikin1967,
author = {Дикин, Илья Иосифович},
file = {:D\:/Mendeley/Дикин - 1967 - Итеративное решение задач линейного и квадратичного программирования.pdf:pdf},
journal = {Доклады Академии наук СССР},
language = {russian},
number = {4},
pages = {747--748},
title = {{Итеративное решение задач линейного и квадратичного программирования}},
url = {https://www.mathnet.ru/rus/dan33112},
volume = {174},
year = {1967}
}
@article{Shor1977,
author = {Шор, Наум Зуселевич},
journal = {Кибернетика},
language = {russian},
number = {1},
pages = {94--95},
title = {{Метод отсечения с растяжением пространства для решения задач выпуклого программирования}},
year = {1977}
}
@article{Deutsch2006:Eng,
abstract = {The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the "convex feasibility" problem. We study the rate of convergence for the cyclic projections algorithm. The notion of angle between convex sets is defined, which generalizes the angle between linear subspaces. The rate of convergence results are described in terms of these angles.},
author = {Deutsch, Frank and Hundal, Hein},
doi = {10.1016/J.JAT.2006.02.005},
file = {:D\:/Mendeley/Deutsch, Hundal - 2006 - The rate of convergence for the cyclic projections algorithm I Angles between convex sets.pdf:pdf},
issn = {0021-9045},
journal = {Journal of Approximation Theory},
keywords = {Alternating projections,Angle between convex sets,Angle between subspaces,Convex feasibility problem,Cyclic projections algorithm,Orthogonal projections,POCS,Projections onto convex sets,Rate of convergence},
number = {1},
pages = {36--55},
publisher = {Academic Press},
title = {{The rate of convergence for the cyclic projections algorithm I: Angles between convex sets}},
volume = {142},
year = {2006}
}
@article{Tank1986:Eng,
abstract = {The rapid solution of several optimization problems by highly interconnected networks of simple analog processors is described. Analog-to-digital (A/D) conversion was considered as a simple optimization problem, and an A/D converter of novel architecture was designed. A/D conversion is a simple example of a more general class of signal-decision problems which, as is shown here, can also be solved by appropriately constructed networks. Circuits to solve these problems were designed using general principles which result from an understanding of the basic collective computational properties of a specific class of analog-processor networks. It is also shown that a network which solves linear programming problems can be understood from the same concepts.},
author = {Tank, D. W. and Hopfield, J. J.},
doi = {10.1109/TCS.1986.1085953},
file = {:D\:/Mendeley//Tank, Hopfield - 1986 - Simple `neural' optimization networks An AD converter, signal decision circuit, and a linear programming circuit.pdf:pdf},
issn = {00984094},
journal = {IEEE transactions on circuits and systems},
number = {5},
pages = {533--541},
title = {{Simple `neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit}},
volume = {CAS-33},
year = {1986}
}
@article{Jeroslow1973:Eng,
abstract = {We extend a result of Klee and Minty by showing that the Simplex Algorithm with the pivot rule of maximizing criterion improvement is not a good algorithm in the sense of Edmonds. The method of proof extends to other similar pivot rules.},
author = {Jeroslow, R.G.},
doi = {10.1016/0012-365X(73)90171-4},
file = {:D\:/Mendeley/Jeroslow - 1973 - The simplex algorithm with the pivot rule of maximizing criterion improvement.pdf:pdf},
issn = {0012-365X},
journal = {Discrete Mathematics},
number = {4},
pages = {367--377},
title = {{The simplex algorithm with the pivot rule of maximizing criterion improvement}},
url = {https://www.sciencedirect.com/science/article/pii/0012365X73901714?via%3Dihub},
volume = {4},
year = {1973}
}
@article{Hartung2018:Eng,
author = {Hartung, T.},
doi = {10.3389/fdata.2018.00005},
file = {:D\:/Mendeley/Hartung - 2018 - Making Big Sense from Big Data.pdf:pdf},
issn = {2624-909X},
journal = {Frontiers in Big Data},
keywords = {Big dara,Learning methods,Medicine,Public Health,artificial intelligence,machine learning},
pages = {5},
title = {{Making Big Sense from Big Data}},
volume = {1},
year = {2018}
}
@article{Kheirfam2016:Eng,
author = {Kheirfam, B. and Haghighi, M.},
doi = {10.1080/02331934.2015.1080255},
file = {:D\:/Mendeley/Kheirfam, Haghighi - 2016 - A full-Newton step infeasible interior-point method for linear optimization based on a trigonometric kernel.pdf:pdf},
issn = {0233-1934},
journal = {Optimization},
number = {4},
pages = {841--857},
publisher = {Informa UK Limited},
title = {{A full-Newton step infeasible interior-point method for linear optimization based on a trigonometric kernel function}},
volume = {65},
year = {2016}
}
@article{Lachhwani2020:Eng,
abstract = {Artificial neural networks or neural networks (NN) are new computational models based on the working of biological neurons of human body. A NN model consists of an interactive system through which external or internal information flows. Nowadays, NN models are being used to deal with complex real problems. On the other hand, mathematical programming problems (MPPs) are a particular class of optimization problems with mathematical structure of objective function(s) and set of constraints. Use of NN models in solving MPPs is a complex area of research and researchers have tried to contribute to apply NN models on different mathematical programming problems. This paper describes classification of MPPs, different neural network models and the detailed literature review on application of NN models for solving different MPPs along with comprehensive analysis on references. Some new research issues and scopes are also discussed on the use of different NN models on MPPs. This paper aims to present the state of art literature review on the use of NNs for solving MPPs with constructive analysis to elaborate future research scope and new directions in this area for future researchers.},
author = {Lachhwani, K.},
doi = {10.1007/s11831-018-09309-5},
file = {:D\:/Mendeley/Lachhwani - 2020 - Application of Neural Network Models for Mathematical Programming Problems A State of Art Review(2).pdf:pdf},
issn = {1134-3060},
journal = {Archives of Computational Methods in Engineering},
pages = {171--182},
title = {{Application of Neural Network Models for Mathematical Programming Problems: A State of Art Review}},
volume = {27},
year = {2020}
}
@article{Zadeh1973:Eng,
author = {Zadeh, N.},
doi = {10.1007/BF01580132},
file = {:D\:/Mendeley/Zadeh - 1973 - A bad network problem for the simplex method and other minimum cost flow algorithms.pdf:pdf},
journal = {Mathematical Programming},
number = {1},
pages = {255--266},
publisher = {Springer},
title = {{A bad network problem for the simplex method and other minimum cost flow algorithms}},
volume = {5},
year = {1973}
}
@article{Khachiyan1980,
author = {Хачиян, Л.Г.},
file = {:D\:/Mendeley/Хачиян - 1980 - Полиномиальные алгоритмы в линейном программировании.pdf:pdf},
journal = {Журнал вычислительной математики и математической физики},
language = {russian},
number = {1},
pages = {51--68},
title = {{Полиномиальные алгоритмы в линейном программировании}},
volume = {20},
year = {1980}
}
@article{Nurminski2016:Eng,
abstract = {It is shown in this paper that under strict complementarity condition, a linear programming problem can be solved by a single orthogonal projection operation onto the cone generated by rows of constraint matrix and corresponding right-hand sides. The efficient projection procedure with the finite termination is provided and computational experiments are reported.},
author = {Nurminski, Evgeni A.},
doi = {10.1007/S10898-015-0337-9},
file = {:D\:/Mendeley/Nurminski - 2016 - Single-projection procedure for linear optimization.pdf:pdf},
issn = {1573-2916},
journal = {Journal of Global Optimization},
keywords = {linear programming,projection algorithm},
number = {1},
pages = {95--110},
publisher = {Springer},
title = {{Single-projection procedure for linear optimization}},
url = {https://link.springer.com/article/10.1007/s10898-015-0337-9},
volume = {66},
year = {2016}
}
@book{Mall2007:Eng,
abstract = {1.Introduction 2.Real-Time Task Scheduling 3.Handling Resource Sharing and Dependencies among Rael-Time Tasks 4.Scheduling Real-Time Tasks in Multiprocessor and Distributed Systems 5.Commercial Real-Time Operating Systems 6.Real-Time Communication 7.Real-Time Databases},
address = {Delhi, India},
author = {Mall, Rajib},
file = {:D\:/Mendeley/Mall - 2007 - Real-Time Systems Theory and Practice.pdf:pdf},
isbn = {978-81-317-0069-3},
pages = {242},
publisher = {Pearson Education},
title = {{Real-Time Systems: Theory and Practice}},
year = {2007}
}
@article{DePierro1985:Eng,
abstract = {An iterative method for solving general systems of linear inequalities is considered. The method, a relaxed generalization of Cimmino's scheme for solving linear systems, was first suggested by Censor and Elfving. Each iterate is obtained as a convex combination of the orthogonal projections of the previous iterate on the half spaces defined by the linear inequalities. The algorithm is particularly suitable for implementation on computers with parallel processors. We prove convergence from any starting point for both consistent and nonconsistent systems (to a feasible point in the first case, and to a weighted least squares type solutions in the second).},
author = {{De Pierro}, Alvaro R. and Iusem, Alfredo N.},
doi = {10.1016/0024-3795(85)90280-0},
file = {:D\:/Mendeley/De Pierro, Iusem - 1985 - A simultaneous projections method for linear inequalities.pdf:pdf},
issn = {00243795},
journal = {Linear Algebra and its Applications},
keywords = {iterative method,parallel processing,system of linear inequalities},
pages = {243--253},
publisher = {North-Holland},
title = {{A simultaneous projections method for linear inequalities}},
volume = {64},
year = {1985}
}
@book{Seregin2014:Eng,
abstract = {The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.},
address = {Singapore},
author = {Seregin, Gregory},
booktitle = {Lecture Notes on Regularity Theory for the Navier-Stokes Equations},
doi = {10.1142/9314},
file = {:D\:/Mendeley/Seregin - 2014 - Lecture notes on regularity theory for the Navier-Stokes equations.pdf:pdf},
isbn = {978-981-4623-40-7},
pages = {268},
publisher = {World Scientific Publishing Company},
title = {{Lecture notes on regularity theory for the Navier-Stokes equations}},
year = {2014}
}
@book{Dantzig1998:Eng,
address = {Princeton, N.J.},
author = {Dantzig, G. B.},
file = {:D\:/Mendeley/Dantzig - 1998 - Linear programming and extensions.pdf:pdf},
keywords = {Linear programming,Simplex method},
pages = {656},
publisher = {Princeton university press},
title = {{Linear programming and extensions}},
year = {1998}
}
@incollection{Hu1994:Eng,
abstract = {This paper presents a projection method for solving an infinite system of linear inequalities. The solution set of the system may be bounded or unbounded, and the interior of the solution set may be empty or nonempty. The method is extended to an infinite system of convex inequalities.},
address = {Boston, MA, USA},
author = {Hu, Hui},
booktitle = {Advances in Optimization and Approximation. Nonconvex Optimization and Its Applications, vol. 1},
doi = {10.1007/978-1-4613-3629-7_9},
editor = {Du, Ding-Zhu and Sun, Jie},
file = {:D\:/Mendeley/Hu - 1994 - A Projection Method for Solving Infinite Systems of Linear Inequalities.pdf:pdf},
pages = {186--194},
publisher = {Springer},
title = {{A Projection Method for Solving Infinite Systems of Linear Inequalities}},
url = {https://link.springer.com/chapter/10.1007/978-1-4613-3629-7_9},
year = {1994}
}
@article{Cimmino1938:Eng,
author = {Cimmino, Gianfranco},
journal = {La Ricerca Scientifica, XVI, Series II, Anno IX, 1},
pages = {326--333},
title = {{Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari}},
year = {1938}
}
@article{Censor1988:Eng,
author = {Censor, Yair and Altschuler, M.D. and Powlis, W.D.},
doi = {10.1088/0266-5611/4/3/006},
file = {:D\:/Mendeley/Censor, Altschuler, Powlis - 1988 - On the use of Cimmino's simultaneous projections method for computing a solution of the inverse prob.pdf:pdf},
issn = {0266-5611},
journal = {Inverse Problems},
number = {3},
pages = {607--623},
publisher = {IOP Publishing},
title = {{On the use of Cimmino's simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning}},
volume = {4},
year = {1988}
}
@article{Sokolinskaya2018a,
abstract = {Работа посвящена исследованию масштабируемости алгоритма Чиммино для решения систем неравенств. Данный алгоритм является типичным представителем класса итерационных проекционных алгоритмов для решения систем линейных уравнений и неравенств. Для аналитического анализа масштабируемости используется модель параллельных вычислений BSF (Bulk Synchronous Farm). Дается представление алгоритма Чиммино в виде операций над списками с использованием функций высшего порядка Map и Reduce. Выводятся аналитические оценки верхней границы масштабируемости алгоритма для многопроцессорных вычислительных систем с распределенной памятью. Приводятся данные о реализация алгоритма Чиммино над списками на языке С++ с использованием программного шаблона BSF и библиотеки параллельного программирования MPI. Демонстрируются результаты масштабных вычислительных экспериментов, выполненных на кластерной вычислительной системе. На основе экспериментальных результатов дается анализ адекватности оценок, полученных аналитическим путем с помощью стоимостных метрик модели BSF.},
author = {Соколинская, И.М. and Соколинский, Л.Б.},
doi = {10.14529/cmse190102},
file = {:D\:/Mendeley/Соколинская, Соколинский - 2019 - Исследование масштабируемости алгоритма Чиммино для решения систем линейных неравенств на кластерных в.pdf:pdf},
journal = {Вестник ЮУрГУ. Серия: Вычислительная математика и информатика},
keywords = {алгоритм Чиммино,итерационный алгоритм,кластерные вычислительные системы,модель параллельных вычислений BSF,оценка масштабируемости,проекционный алгоритм,релаксация,система линейных неравенств,эффективность распараллеливания},
language = {russian},
number = {1},
pages = {20--35},
title = {{Исследование масштабируемости алгоритма Чиммино для решения систем линейных неравенств на кластерных вычислительных системах}},
url = {https://vestnik.susu.ru/cmi/article/view/7457},
volume = {8},
year = {2019}
}
@article{Gondzio2012:Eng,
abstract = {Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension. Interior point methods are competitive when dealing with small problems of dimensions below one million constraints and variables and are beyond competition when applied to large problems of dimensions going into millions of constraints and variables. In this survey we will discuss several issues related to interior point methods including the proof of the worst-case complexity result, the reasons for their amazingly fast practical convergence and the features responsible for their ability to solve very large problems. The ever-growing sizes of optimization problems impose new requirements on optimization methods and software. In the final part of this paper we will therefore address a redesign of interior point methods to allow them to work in a matrix-free regime and to make them well-suited to solving even larger problems.},
author = {Gondzio, Jacek},
doi = {10.1016/j.ejor.2011.09.017},
file = {:D\:/Mendeley/Gondzio - 2012 - Interior point methods 25 years later.pdf:pdf},
issn = {03772217},
journal = {European Journal of Operational Research},
keywords = {Implementation,Interior point methods,Linear programming,Matrix-free methods,Quadratic programming,Worst-case complexity analysis},
number = {3},
pages = {587--601},
publisher = {Elsevier B.V.},
title = {{Interior point methods 25 years later}},
volume = {218},
year = {2012}
}
@incollection{Kopetz2011-10:Eng,
abstract = {Many thousands of research papers have been written about how to schedule a set of tasks in a system with a limited amount of resources such that all tasks will meet their deadlines. This chapter tries to summarize some important results of scheduling research that...},
address = {New York},
author = {Kopetz, Hermann},
booktitle = {Real-Time Systems: Design Principles for Distributed Embedded Applications},
chapter = {10},
doi = {10.1007/978-1-4419-8237-7_10},
file = {:D\:/Mendeley/Kopetz - 2011 - Real-Time Scheduling.pdf:pdf},
isbn = {978-1-4419-8237-7},
pages = {239--258},
publisher = {Springer},
title = {{Real-Time Scheduling}},
year = {2011}
}
@incollection{Mamalis2015:Eng,
abstract = {The simplex method has been successfully used in solving linear programming problems for many years. Parallel approaches for the simplex method have been extensively studied in the literature due to the intensive computations required, especially for the solution of large linear problems (LPs). In this paper, first a detailed overview is given of the parallelization attempts concerning the standard and the revised simplex method made to date. Next, some of the most recent and significant relevant attempts are selected and presented in more detail along with experimental results. The latter include some impressive results obtained for the revised simplex method over a modern supercomputer, as well as the recent advances in GPU-based related attempts.},
address = {City: Cham},
author = {Mamalis, B. and Pantziou, G.},
booktitle = {Algorithms, Probability, Networks, and Games. Lecture Notes in Computer Science, vol. 9295},
doi = {10.1007/978-3-319-24024-4_17},
editor = {Zaroliagis, C. and Pantziou, G. and Kontogiannis, S.},
file = {:D\:/Mendeley/Mamalis, Pantziou - 2015 - Advances in the Parallelization of the Simplex Method.pdf:pdf},
keywords = {Linear programming,parallel simplex},
pages = {281--307},
publisher = {Springer},
title = {{Advances in the Parallelization of the Simplex Method}},
year = {2015}
}
@book{Kopanos2019:Eng,
abstract = {Explains and demonstrates techniques for solving large-scale production scheduling and planning problems in the process industries Bridges the gap between theory and practice in planning and scheduling Includes 78 illustrations, additional online material, and case studies highlighting real-world applications at leading firms in the process industry.},
address = {Cham, Switzerland},
author = {Kopanos, Georgios M. and Puigjaner, Luis},
booktitle = {Solving Large-Scale Production Scheduling and Planning in the Process Industries},
doi = {10.1007/978-3-030-01183-3},
file = {:D\:/Mendeley/Kopanos, Puigjaner - 2019 - Solving Large-Scale Production Scheduling and Planning in the Process Industries.pdf:pdf},
isbn = {9783030011833},
keywords = {Engineering Economics,Large-Scale Planning,Performance Optimization,Process Industries,Process Systems Engineering,Production Scheduling},
pages = {1--291},
publisher = {Springer},
title = {{Solving Large-Scale Production Scheduling and Planning in the Process Industries}},
year = {2019}
}
@article{Rodriguez-Vazquez1990:Eng,
abstract = {A systematic approach is presented for the design of analog “neural” nonlinear programming solvers using switched-capacitor (SC) integrated circuit techniques. The method is based on formulating a dynamic gradient system whose state evolves in time towards the solution point of the corresponding programming problem. A “neuron” cell for the linear and the quadratic problem suitable for monolithic implementation is introduced. The design of this “neuron” and its corresponding “synapses” using switched-capacitor techniques are considered in detail. A SC circuit architecture based on a reduced set of basic building blocks with high modularity is presented. Simulation results using a mixed-mode simulator (DIANA) [1] and experimental results from breadboard prototypes are included, illustrating the validity of the proposed techniques. {\textcopyright} 1990 IEEE},
author = {Rodriguez-Vazquez, A. and Dominguez-Castro, R. and Rueda, A. and Huertas, J. L. and Sanchez-Sinencio, E.},
doi = {10.1109/31.52732},
file = {:D\:/Mendeley//Rodriguez-Vazquez et al. - 1990 - Nonlinear Switched-Capacitor ``Neural'' Networks for Optimization Problems.pdf:pdf},
issn = {00984094},
journal = {IEEE Transactions on Circuits and Systems},
number = {3},
pages = {384--398},
title = {{Nonlinear Switched-Capacitor ``Neural'' Networks for Optimization Problems}},
volume = {37},
year = {1990}
}
@book{Chinneck2008:Eng,
abstract = {Constrained optimization models are core tools in business, science, government, and the military with applications including airline scheduling, control of petroleum refining operations, investment decisions, and many others. Constrained optimization models have grown immensely in scale and complexity in recent years as inexpensive computing power has become widely available. Models now frequently have many complicated interacting constraints, giving rise to a host of issues related to feasibility and infeasibility. For example, it is sometimes difficult to find any feasible point at all for a large model, or even to accurately determine if one exists, e.g. for nonlinear models. If the model is feasible, how quickly can a solution be found? If the model is infeasible, how can the cause be isolated and diagnosed? Can a repair to restore feasibility be carried out automatically? Researchers have developed numerous algorithms and computational methods in recent years to address such issues, with a number of surprising spin-off applications in fields such as artificial intelligence and computational biology. Over the same time period, related approaches and techniques relating to feasibility and infeasibility of constrained problems have arisen in the constraint programming community. Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, nonlinear, and mixed-integer programs. Connections to related work in constraint programming are shown. Part I of the book addresses algorithms for seeking feasibility quickly, including new methods for the difficult cases of nonlinear and mixed-integer programs. Part II provides algorithms for analyzing infeasibility by isolating minimal infeasible (or maximum feasible) subsets of constraints, or by finding the best repair for the infeasibility. Infeasibility analysis algorithms have arisen primarily over the last two decades, and the book covers these in depth and detail. Part III describes applications in numerous areas outside of direct infeasibility analysis such as finding decision trees for data classification, analyzing protein folding, radiation treatment planning, automated test assembly, etc. A main goal of the book is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems.},
address = {New York},
author = {Chinneck, John W.},
booktitle = {Feasibility and Infeasibility in Optimization},
doi = {10.1007/978-0-387-74932-7},
file = {:D\:/Mendeley/Chinneck - 2008 - Feasibility and Infeasibility in Optimization Algorithms and Computational Methods.pdf:pdf},
isbn = {978-0-387-74932-7},
keywords = {feasibility problem},
pages = {XXII, 274},
publisher = {Springer},
title = {{Feasibility and Infeasibility in Optimization: Algorithms and Computational Methods}},
year = {2008}
}
@article{Eremin2009,
author = {Ерёмин, И. И. and Попов, Л. Д.},
file = {:D\:/Mendeley/Ерёмин, Попов - 2009 - Фейеровские процессы в теории и практике обзор последних результатов.pdf:pdf},
journal = {Известия вузов. Математика},
language = {russian},
number = {1},
pages = {44--65},
title = {{Фейеровские процессы в теории и практике: обзор последних результатов}},
url = {https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=1253},
year = {2009}
}
@article{Sokolinskaya2020,
abstract = {Статья посвящена исследованию нового метода решения сверхбольших задач линейного программирования. Указанный метод получил название "апекс-метод". Апекс-метод работает по схеме предиктор-корректор. На фазе предиктор находится точка, лежащая на границе ?мерного многогранника, задающего допустимую область задачи линейного программирования. На фазе корректор организуется итерационный процесс, в результате которого строится последовательность точек, сходящаяся к точному решению задачи линейного программирования. В статье дается формальное описание апекс-метода и приводятся сведения о его параллельной реализации на языке C++ с использованием библиотеки MPI. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе по исследованию масштабируемости апекс-метода.},
author = {Соколинская, Ирина М. and Соколинский, Леонид Б.},
doi = {10.26089/NumMet.v21r328},
file = {:D\:/Mendeley/Соколинская, Соколинский - 2020 - Об одном итерационном методе решения задач линейного программирования на кластерных вычислительных сис.pdf:pdf},
journal = {Вычислительные методы и программирование},
keywords = {апекс-метод,задача линейного программирования большой размерно,итерационный метод,кластерная вычислительная система,линейное программирование,параллельный алгоритм,схема предиктор-корректор},
language = {russian},
number = {4},
pages = {329--340},
title = {{Об одном итерационном методе решения задач линейного программирования на кластерных вычислительных системах}},
volume = {21},
year = {2020}
}
@article{Olkhovsky2022,
author = {Ольховский, Николай Александрович and Соколинский, Леонид Борисович},
doi = {10.14529/cmse220103},
file = {:D\:/Mendeley/Ольховский, Соколинский - 2022 - Визуальное представление многомерных задач линейного программирования.pdf:pdf},
journal = {Вестник ЮУрГУ. Серия: Вычислительная математика и информатика},
language = {russian},
number = {1},
pages = {31--56},
title = {{Визуальное представление многомерных задач линейного программирования}},
volume = {11},
year = {2022}
}
@incollection{Bartels1971:Eng,
abstract = {loss of precision, simplex method},
address = {Berlin, Heidelberg},
author = {Bartels, R.H. and Stoer, J. and Zenger, Ch.},
booktitle = {Handbook for Automatic Computation. Volume II: Linear Algebra},
doi = {10.1007/978-3-642-86940-2_11},
file = {:D\:/Mendeley/Bartels, Stoer, Zenger - 1971 - A Realization of the Simplex Method Based on Triangular Decompositions.pdf:pdf},
pages = {152--190},
publisher = {Springer},
title = {{A Realization of the Simplex Method Based on Triangular Decompositions}},
year = {1971}
}
@inproceedings{Gondzio2006:Eng,
abstract = {Solution methods for very large scale optimization problems are addressed in this paper. Interior point methods are demonstrated to provide unequalled efficiency in this context. They need a small (and predictable) number of iterations to solve a problem. A single iteration of interior point method requires the solution of indefinite system of equations. This system is regularized to guarantee the existence of triangular decomposition. Hence the well-understood parallel computing techniques developed for positive definite matrices can be extended to this class of indefinite matrices. A parallel implementation of an interior point method is described in this paper. It uses object-oriented programming techniques and allows for exploiting different block-structures of matrices. Our implementation outperforms the industry-standard optimizer, shows very good parallel efficiency on massively parallel architecture and solves problems of unprecedented sizes reaching 109 variables.},
address = {Berlin, Heidelberg},
author = {Gondzio, Jacek and Grothey, Andreas},
booktitle = {Parallel Processing and Applied Mathematics. PPAM 2005. Lecture Notes in Computer Science, vol. 3911},
doi = {10.1007/11752578_62},
editor = {Wyrzykowski, R. and Dongarra, J. and Meyer, N. and Wasniewski, J.},
file = {:D\:/Mendeley/Gondzio, Grothey - 2006 - Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods.pdf:pdf},
isbn = {3540341412},
issn = {03029743},
keywords = {Direct Solution,Interior Point Algorithm,Interior Point Method,Jacobian Matrice,Portfolio Selection},
pages = {513--525},
publisher = {Springer},
title = {{Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods}},
volume = {3911 LNCS},
year = {2006}
}
@article{Kaczmarz1937:Eng,
author = {Kaczmarz, Stefan},
journal = {Bulletin International de l'Acadmie Polonaise des Sciences et des Lettres. Classe des Sciences Mathmatiques et Naturelles. Srie A, Sciences Mathmatiques},
pages = {355--357},
title = {{Angenherte Auflsung von Systemen linearer Gleichungen}},
volume = {35},
year = {1937}
}
@article{Jagadish2014:Eng,
author = {Jagadish, H. V. and Gehrke, J. and Labrinidis, A. and Papakonstantinou, Y. and Patel, Jignesh M. and Ramakrishnan, R. and Shahabi, C.},
doi = {10.1145/2611567},
file = {:D\:/Mendeley/Jagadish et al. - 2014 - Big data and its technical challenges.pdf:pdf},
issn = {00010782},
journal = {Communications of the ACM},
number = {7},
pages = {86--94},
title = {{Big data and its technical challenges}},
volume = {57},
year = {2014}
}
@incollection{Fejer1982:Eng,
address = {Berlin, Heidelberg},
author = {Fejer, Leopold},
booktitle = {Festschrift},
doi = {10.1007/978-3-642-61810-9_6},
file = {:D\:/Mendeley/Fejer - 1982 - Uber die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Art entspringen.pdf:pdf},
keywords = {Fejer mapping},
mendeley-tags = {Fejer mapping},
pages = {41--48},
publisher = {SpringerVerlag},
title = {{Uber die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Art entspringen}},
url = {https://link.springer.com/chapter/10.1007%2F978-3-642-61810-9_6 http://link.springer.com/10.1007/978-3-642-61810-9_6},
year = {1982}
}
@article{Yudin1976:Rus,
author = {Юдин, Давид Беркович and Немировский, Аркадий Семёнович},
journal = {Экономика и математические методы},
language = {russian},
number = {2},
pages = {357--369},
title = {{Информационная сложность и эффективные методы решения выпуклых экстремальных задач}},
year = {1976}
}
@book{Eremin1979:Rus,
abstract = {Книга посвящена разработке аппарата моделирования и оптимизации сложных эволюционирующих систем средствами итерационных процессов математического программирования, приспособленных к учёту нестационарности тех или иных элементов модели, а также учёту их плохой формализуемости. Последнее осуществляется с помощью математических процедур распознавания образов. Рассматриваемые в книге методы могут быть применены, с одной стороны, к решению обычных задач математического программирования, а с другой стороны - к решению плохо определённых задач оптимизации. Нестационарные процессы математического программирования могут выступать как средство моделирования и оптимизации конкретных развивающихся систем: экономических, технических, биологических и др.},
address = {М.},
author = {Ерёмин, Иван Иванович and Мазуров, Владимир Данилович},
file = {:D\:/Mendeley/Ерёмин, Мазуров - 1979 - Нестационарные процессы математического программирования.pdf:pdf},
language = {russian},
pages = {288},
publisher = {Наука. Главная редакция физико-математической литературы},
title = {{Нестационарные процессы математического программирования}},
year = {1979}
}
@book{Nesterov1994:Eng,
abstract = {Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs. The book contains new and important results in the general theory of convex programming, e.g., their “conic” problem formulation in which duality theory is completely symmetric. For each algorithm described, the authors carefully derive precise bounds on the computational effort required to solve a given family of problems to a given precision. In several cases they obtain better problem complexity estimates than were previously known. Several of the new algorithms described in this book, e.g., the projective method, have been implemented, tested on “real world” problems, and found to be extremely efficient in practice.},
author = {Nesterov, Yurii and Nemirovskii, Arkadii},
doi = {10.1137/1.9781611970791},
isbn = {978-0-89871-319-0},
keywords = {approximation,convex programming,interior-point methods,optimization,quadratic programming},
month = {jan},
pages = {ix + 396},
publisher = {Society for Industrial and Applied Mathematics},
title = {{Interior-Point Polynomial Algorithms in Convex Programming}},
url = {http://epubs.siam.org/doi/book/10.1137/1.9781611970791},
year = {1994}
}
@article{Motzkin1954:Eng,
author = {Motzkin, Theodore Samuel and Schoenberg, I. J.},
doi = {10.4153/CJM-1954-038-x},
file = {:D\:/Mendeley/Motzkin, Schoenberg - 1954 - The relaxation method for linear inequalities.pdf:pdf},
issn = {0008-414X},
journal = {Canadian Journal of Mathematics},
keywords = {Relaxation method,system of linear inequalities},
pages = {393--404},
title = {{The relaxation method for linear inequalities}},
volume = {6},
year = {1954}
}
@book{Vasin2005,
address = {Екатеринбург},
author = {Васин, Владимир Васильевич and Ерёмин, Иван Иванович},
isbn = {5769115637},
language = {russian},
pages = {211},
publisher = {УрО РАН},
title = {{Операторы и итерационные процессы фейеровского типа. Теория и приложения}},
year = {2005}
}
@inproceedings{Zagoskina2019:Eng,
abstract = {The paper suggests an approach to creating intelligent blast furnace performance control system. This system is based on the analysis of statistical data on the operation of a blast furnace over several years. Cluster analysis is proposed as the main approach to big data processing. Cluster analysis reveals hidden relationships in data. In addition, this approach allows to determine the operation mode of the blast furnace despite a large set of input parameters. Kohonen neural network was chosen for clustering. In this paper, the results are blast furnace operating modes by blast parameters. The article also presents the concept of an expert system. An expert system based on cluster partitioning data allows to evaluate the efficiency of the furnace according to the criterion of maximum productivity and minimum coke consumption. Besides, this system allows to rely on calculations when planning the work of the workshop for a given time period.},
author = {Zagoskina, E. V. and Barbasova, T. A. and Shnaider, D. A.},
booktitle = {SIBIRCON 2019 - International Multi-Conference on Engineering, Computer and Information Sciences, Proceedings},
doi = {10.1109/SIBIRCON48586.2019.8958221},
isbn = {9781728144016},
keywords = {Kohonen neural network,blast furnace production,cluster analysis,expert system,iron smelting},
pages = {710--713},
publisher = {IEEE},
title = {{Intelligent Control System of Blast-furnace Melting Efficiency}},
year = {2019}
}
@article{Kennedy1987:Eng,
abstract = {The linear programming network of Tank and Hopfield is shown to obey the same unifying stationary cocontent theorem as the canonical nonlinear programming circuit of Chua and Lin. Application of this theorem highlights an error in the design of Tank and Hopfield and suggests how this can be corrected to guarantee the existence of a bounded solution. The accuracy of the solution is maximized when the circuit of Tank and Hopfield reduces to the simplest special case of the canonical nonlinear programming circuit. {\textcopyright} 1987 IEEE},
author = {Kennedy, M. P. and Chua, L. O.},
doi = {10.1109/TCS.1987.1086095},
file = {:D\:/Mendeley/Kennedy, Chua - 1987 - Unifying the Tank and Hopfield Linear Programming Circuit and the Canonical Nonlinear Programming Circuit of Chua.pdf:pdf},
issn = {00984094},
journal = {IEEE Transactions on Circuits and Systems},
number = {2},
pages = {210--214},
title = {{Unifying the Tank and Hopfield Linear Programming Circuit and the Canonical Nonlinear Programming Circuit of Chua and Lin}},
volume = {34},
year = {1987}
}
@article{Gonzalez-Gutierrez2011b:Eng,
abstract = {The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. Different schemes of numerical methods, which solve the feasibility problem in the finite linear programming, have been proposed in [1]. In this paper, we consider the so-called under and over projection scheme in the semi-infinite case. We construct a class of methods and prove their convergence. For the same class of the extended relaxation methods, we have shown that the rate of convergence is linear.},
author = {Gonzalez-Gutierrez, Enrique and {Hernandez Rebollar}, Lidia A. and Todorov, Maxim I.},
file = {:D\:/Mendeley/Gonzalez-Gutierrez, Hernandez Rebollar, Todorov - 2011 - Under and over projection methods for solving linear inequality systems.pdf:pdf},
issn = {13101331},
journal = {Comptes Rendus de L'Academie Bulgare des Sciences},
keywords = {Feasibility problem,Linear inequality systems,Numerical methods},
number = {6},
pages = {785--790},
title = {{Under and over projection methods for solving linear inequality systems}},
volume = {64},
year = {2011}
}
@article{Lubin2013:Eng,
abstract = {We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.},
author = {Lubin, Miles and Hall, J. A. Julian and Petra, Cosmin G. and Anitescu, Mihai},
doi = {10.1007/s10589-013-9542-y},
file = {:D\:/Mendeley/Lubin et al. - 2013 - Parallel distributed-memory simplex for large-scale stochastic LP problems.pdf:pdf},
issn = {0926-6003},
journal = {Computational Optimization and Applications},
keywords = {Block-angular,Parallel computing,Simplex method,Stochastic optimization},
number = {3},
pages = {571--596},
title = {{Parallel distributed-memory simplex for large-scale stochastic LP problems}},
url = {http://link.springer.com/10.1007/s10589-013-9542-y},
volume = {55},
year = {2013}
}
@incollection{Cheng2002:Eng,
address = {Hoboken, New Jersey},
author = {Cheng, Albert M. K.},
booktitle = {Real-Time Systems: Scheduling, Analysis, and Verification},
chapter = {3},
doi = {10.1002/0471224626.CH3},
file = {:D\:/Mendeley/Cheng - 2002 - Real-Time Scheduling and Schedulability Analysis.pdf:pdf},
isbn = {9780471224624},
keywords = {case execution time (WCET),computation time prediction,deadline,dynamic,earliest,first (EDF) algorithm,first (LL) algorithm,fixed,laxity,least,monotonic (DM) algorithm,monotonic (RM) algorithm,multiprocessor scheduling,priority schedulers,rate,real,schedulability analysis,time operating systems (RTOSs),time scheduling,worst},
pages = {41--85},
publisher = {John Wiley and Sons},
title = {{Real-Time Scheduling and Schedulability Analysis}},
year = {2002}
}
@inproceedings{Yuan2011:Eng,
abstract = {The modern era of interior-point methods (IPM) dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, interior-point algorithm and software for linear problems have become quite sophisticated and gained extraordinary interest as an alternative to the sparse simplex based methods. In this paper, we introduce the infeasible primal-dual algorithm which is widely considered the most efficient general purpose IPM. Then many issues that are crucial for the efficient implementation of an interior-point algorithm are addressed in detail. To facilitate the understanding of different implementation strategies, some illustrative numerical results on a subset of problems from the Netlib collection are presented.},
author = {Yuan, Y.},
booktitle = {Proc. SPIE, vol. 8285. International Conference on Graphic and Image Processing (ICGIP 2011)},
doi = {10.1117/12.913019},
file = {:D\:/Mendeley/Yuan - 2011 - Implementation tricks of interior-point methods for large-scale linear programs.pdf:pdf},
keywords = {Implementation Tricks,Interior-Point Methods,Large-Scale Linear Programs},
publisher = {International Society for Optics and Photonics},
title = {{Implementation tricks of interior-point methods for large-scale linear programs}},
year = {2011}
}
@article{Prieto2016:Eng,
abstract = {This paper presents a comprehensive overview of modelling, simulation and implementation of neural networks, taking into account that two aims have emerged in this area: the improvement of our understanding of the behaviour of the nervous system and the need to find inspiration from it to build systems with the advantages provided by nature to perform certain relevant tasks. The development and evolution of different topics related to neural networks is described (simulators, implementations, and real-world applications) showing that the field has acquired maturity and consolidation, proven by its competitiveness in solving real-world problems. The paper also shows how, over time, artificial neural networks have contributed to fundamental concepts at the birth and development of other disciplines such as Computational Neuroscience, Neuro-engineering, Computational Intelligence and Machine Learning. A better understanding of the human brain is considered one of the challenges of this century, and to achieve it, as this paper goes on to describe, several important national and multinational projects and initiatives are marking the way to follow in neural-network research.},
author = {Prieto, Alberto and Prieto, Beatriz and Ortigosa, Eva Martinez and Ros, Eduardo and Pelayo, Francisco and Ortega, Julio and Rojas, Ignacio},
doi = {10.1016/j.neucom.2016.06.014},
file = {:D\:/Mendeley/Prieto et al. - 2016 - Neural networks An overview of early research, current frameworks and new challenges.pdf:pdf},
issn = {09252312},
journal = {Neurocomputing},
keywords = {Applications of neural networks,Artificial neural networks,Brain Initiative,Human Brain Project,Learning algorithms,Neural hardware,Neural modelling,Neural networks,Neural simulators,survey},
pages = {242--268},
publisher = {Elsevier},
title = {{Neural networks: An overview of early research, current frameworks and new challenges}},
volume = {214},
year = {2016}
}
@article{Sokolinsky2021b,
author = {Соколинский, Леонид Борисович and Соколинская, Ирина Михайловна},
doi = {10.14529/cmse210103},
file = {:D\:/Mendeley/Соколинский, Соколинская - 2021 - О генерации случайных задач линейного программирования на кластерных вычислительных системах.pdf:pdf},
issn = {23059052},
journal = {Вестник Южно-Уральского государственного университета. Серия: Вычислительная математика и информатика},
language = {russian},
number = {2},
pages = {38--52},
title = {{О генерации случайных задач линейного программирования на кластерных вычислительных системах}},
volume = {10},
year = {2021}
}
@article{Gubin1967:Eng,
abstract = {MANY mathematical and applied problems can be reduced to finding some common point of a system (finite or infinite) of convex sets. Usually each of the sets is such that it is not difficult to find the projection of any point on to this set. In this paper we shall consider various methods of finding points from the intersection of sets, using projection on to a separate set as an elementary operation. The strong convergence of the sequences obtained in this way is proved. Applications are given to various problems, including the problem of best approximation and problems of optimal control. Particular attention is paid in the latter case to problems with restrictions on the phase coordinates.},
author = {Gubin, L.G. and Polyak, B.T. and Raik, E.V.},
doi = {10.1016/0041-5553(67)90113-9},
file = {:D\:/Mendeley/Gubin, Polyak, Raik - 1967 - The method of projections for finding the common point of convex sets.pdf:pdf},
issn = {00415553},
journal = {USSR Computational Mathematics and Mathematical Physics},
keywords = {intersection of convex sets,metod of projections,relaxation method},
month = {jan},
number = {6},
pages = {1--24},
publisher = {No longer published by Elsevier},
title = {{The method of projections for finding the common point of convex sets}},
url = {https://www.sciencedirect.com/science/article/pii/0041555367901139?via%3Dihub http://linkinghub.elsevier.com/retrieve/pii/0041555367901139},
volume = {7},
year = {1967}
}
@article{Yang1992:Eng,
abstract = {New iterative methods for solving systems of linear inequalities are presented. Each step in these methods consists of finding the orthogonal projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints. Both sequential and parallel implementations are discussed.},
author = {Yang, K. and Murty, K. G.},
doi = {10.1007/BF00939954},
file = {:D\:/Mendeley/Yang, Murty - 1992 - New iterative methods for linear inequalities.pdf:pdf},
issn = {0022-3239},
journal = {Journal of Optimization Theory and Applications},
keywords = {iterative methods,linear inequalities,paralleI implementation,sequential implementation,surrogate constraints},
number = {1},
pages = {163--185},
publisher = {Kluwer Academic Publishers-Plenum Publishers},
title = {{New iterative methods for linear inequalities}},
url = {http://link.springer.com/10.1007/BF00939954},
volume = {72},
year = {1992}
}
@article{Fathi-Hafshejani2018:Eng,
abstract = {In this paper, we propose a large-update primal–dual interior-point algorithm for linear optimization problems based on a new kernel function with a trigonometric growth term. By simple analysis, we prove that in the large neighbourhood of the central path, the worst case iteration complexity of the new algorithm is bounded above by (Formula presented.), which matches the currently best known iteration bound for large-update methods. Moreover, we show that, most of the so far proposed kernel functions can be rewritten as a kernel function with trigonometric growth term. Finally, numerical experiments on some test problems confirm that the new kernel function is well promising in practice in comparison with some existing kernel functions in the literature.},
author = {Fathi-Hafshejani, S. and Mansouri, H. and {Reza Peyghami}, M. and Chen, S.},
doi = {10.1080/02331934.2018.1482297},
file = {:D\:/Mendeley/Fathi-Hafshejani et al. - 2018 - Primal–dual interior-point method for linear optimization based on a kernel function with trigonometric.pdf:pdf},
issn = {10294945},
journal = {Optimization},
keywords = {Kernel function,Large-update methods,linear optimization,primal–dual interior-point methods,trigonometric growth term},
number = {10},
pages = {1605--1630},
title = {{Primal–dual interior-point method for linear optimization based on a kernel function with trigonometric growth term}},
volume = {67},
year = {2018}
}
@article{Keil2006:Eng,
abstract = {The Netlib library of linear programming problems is a well known suite containing many real world applications. Recently it was shown by Ord{\'{o}}{\~{n}}ez and Freund that 71\% of these problems are ill-conditioned. Hence, numerical difficulties may occur. Here, we present rigorous results for this library that are computed by a verification method using interval arithmetic. In addition to the original input data of these problems we also consider interval input data. The computed rigorous bounds and the performance of the algorithms are related to the distance to the next ill-posed linear programming problem.},
author = {Keil, Christian and Jansson, Christian},
doi = {10.1007/S11155-006-9004-7/METRICS},
file = {:D\:/Mendeley/Keil, Jansson - 2006 - Computational experience with rigorous error bounds for the netlib linear programming library.pdf:pdf},
issn = {13853139},
journal = {Reliable Computing},
keywords = {Approximations and Expansions,Computational Mathematics and Numerical Analysis,Mathematical Modeling and Industrial Mathematics,Numeric Computing},
number = {4},
pages = {303--321},
publisher = {Springer},
title = {{Computational experience with rigorous error bounds for the netlib linear programming library}},
volume = {12},
year = {2006}
}
@article{Aharoni1989:Eng,
abstract = {An iterative method is proposed for solving convex feasibility problems. Each iteration is a convex combination of projections onto the given convex sets where the weights of the combination may vary from step to step. It is shown that any sequence of iterations generated by the algorithm converges if the intersection of the given family of convex sets is nonempty and that the limit point of the sequence belongs to this intersection under mild conditions on the sequence of weight functions. Special cases are block-iterative processes where in each iterative step a certain subfamily of the given family of convex sets is used. In particular, a block-iterative version of the Agmon-Motzkin-Schoenberg relaxation method for solving systems of linear inequalities is derived. Such processes lend themselves to parallel implementation and will be useful in various areas of applications, including image reconstruction from projections, image restoration, and other fully discretized inversion problems.},
author = {Aharoni, Ron and Censor, Yair},
doi = {10.1016/0024-3795(89)90375-3},
file = {:D\:/Mendeley/Aharoni, Censor - 1989 - Block-iterative projection methods for parallel computation of solutions to convex feasibility problems.pdf:pdf},
issn = {00243795},
journal = {Linear Algebra and its Applications},
keywords = {convex feasibility problem,parallel implementation,relaxation method},
pages = {165--175},
publisher = {North-Holland},
title = {{Block-iterative projection methods for parallel computation of solutions to convex feasibility problems}},
volume = {120},
year = {1989}
}
@article{Xu2016:Eng,
abstract = {Based on an equivalent reformulation of the central path, we ob-tain a modified-Newton step for linear optimization. Using this step, we pro-pose an infeasible interior-point algorithm. The algorithm uses only one full-modified-Newton step search in each iteration. The complexity bound of the algorithm is the best known for infeasible interior-point algorithm.},
author = {Xu, Yinghong and Zhang, Lipu and Zhang, Jing},
doi = {10.3934/jimo.2016.12.103},
file = {:D\:/Mendeley/Xu, Zhang, Zhang - 2016 - A full-modified-newton step infeasible interior-point algorithm for linear optimization.pdf:pdf},
issn = {1553166X},
journal = {Journal of Industrial and Management Optimization},
keywords = {Complexity analysis,Full-Newton step,Infeasible interior-point algorithm,Linear optimization,Modified-Newton-direction},
number = {1},
pages = {103--116},
publisher = {American Institute of Mathematical Sciences},
title = {{A full-modified-newton step infeasible interior-point algorithm for linear optimization}},
volume = {12},
year = {2016}
}
@article{Gould2008:Eng,
abstract = {We consider simple projection methods for solving convex feasibility problems. Both successive and sequential methods are considered, and heuristics to improve these are suggested. Unfortunately, particularly given the large literature which might make one think otherwise, numerical tests indicate that in general none of the variants considered are especially effective or competitive with more sophisticated alternatives.},
author = {Gould, Nicholas I.M.},
doi = {10.1007/S10589-007-9073-5},
file = {:D\:/Mendeley/Gould - 2008 - How good are projection methods for convex feasibility problems.pdf:pdf},
issn = {1573-2894},
journal = {Computational Optimization and Applications},
keywords = {Convex and Discrete Geometry,Management Science,Operations Research,Operations Research/Decision Theory,Optimization,Statistics,general},
number = {1},
pages = {1--12},
publisher = {Springer},
title = {{How good are projection methods for convex feasibility problems?}},
url = {https://link.springer.com/article/10.1007/s10589-007-9073-5},
volume = {40},
year = {2008}
}
@article{Censor1985:Eng,
abstract = {The problem of solving iteratively a large and possibly sparse system of interval linear inequalities is considered. An algorithm of the row-action type is proposed which, in each iterative step, effectively takes account of a pair of inequalities describing a single interval inequality. The algorithm realizes in an automatic manner a relaxation principle proposed by Goffin but also allows further external relaxation parameters.},
author = {Censor, Yair},
doi = {10.1016/0022-247X(85)90127-1},
file = {:D\:/Mendeley/Censor - 1985 - An automatic relaxation method for solving interval linear inequalities.pdf:pdf},
issn = {10960813},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Relaxation method,system of linear inequalities},
number = {1},
pages = {19--25},
title = {{An automatic relaxation method for solving interval linear inequalities}},
volume = {106},
year = {1985}
}
@article{Agmon1954:Eng,
author = {Agmon, Shmuel},
doi = {10.4153/CJM-1954-037-2},
file = {:D\:/Mendeley/Agmon - 1954 - The relaxation method for linear inequalities.pdf:pdf},
issn = {1496-4279},
journal = {Canadian Journal of Mathematics},
keywords = {Relaxation method,system of linear inequalities},
pages = {382--392},
title = {{The relaxation method for linear inequalities}},
volume = {6},
year = {1954}
}
@book{Gastinel1971:Eng,
address = {New York},
author = {Gastinel, Noel},
pages = {ix+341},
publisher = {Academic Press},
title = {{Linear Numerical Analysis}},
year = {1971}
}
@article{Sokolinsky2023,
author = {Соколинский, Леонид Борисович and Соколинская, Ирина Михайловна},
doi = {10.14529/cmse230201},
file = {:D\:/Mendeley/Соколинский, Соколинская - 2023 - О новой версии апекс-метода для решения задач линейного программирования.pdf:pdf},
journal = {Вестник ЮУрГУ. Серия: Вычислительная математика и информатика},
language = {russian},
number = {2},
pages = {5--46},
title = {{О новой версии апекс-метода для решения задач линейного программирования}},
volume = {12},
year = {2023}
}
@incollection{Censor2016:Eng,
abstract = {Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same feasiblity-seeking iterative process without superiorization. Using a feasibility-seeking iterative process that converges even if the linear feasible set is empty, LinSup generates an iterative sequence that converges to a point that minimizes a proximity function which measures the linear constraints violation. In addition, due to LinSup's repeated objective function reduction steps such a point will most probably have a reduced objective function value. We present an exploratory experimental result that illustrates the behavior of LinSup on an infeasible LP problem.},
address = {City: Cham},
author = {Censor, Yair and Zur, Yehuda},
booktitle = {Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science. Vol. 9869},
doi = {10.1007/978-3-319-44914-2_2},
editor = {Kochetov, Y. and Khachay, M. and Beresnev, V. and Nurminski, E. and Pardalos, P.},
file = {:D\:/Mendeley/Censor, Zur - 2016 - Linear Superiorization for Infeasible Linear Programming.pdf:pdf},
keywords = {Cimmino method,feasibility-seeking,infeasible linear programming,perturbation resilience,proximity function,simultaneous projection algorithm,superiorization},
pages = {15--24},
publisher = {Springer},
title = {{Linear Superiorization for Infeasible Linear Programming}},
url = {http://link.springer.com/10.1007/978-3-319-44914-2_2},
year = {2016}
}
@article{Censor2017:Eng,
abstract = {Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: 'yes' and 'very well', respectively.},
author = {Censor, Yair},
doi = {10.1088/1361-6420/33/4/044006},
file = {:D\:/Mendeley/Censor - 2017 - Can linear superiorization be useful for linear optimization problems.pdf:pdf},
issn = {0266-5611},
journal = {Inverse Problems},
keywords = {Agmon–Motzkin–Schoenberg algorithm,Simplex algorithm,bounded perturbation resilience,feasibility-seeking,linear programming,superiorization},
number = {4},
pages = {044006},
publisher = {IOP Publishing},
title = {{Can linear superiorization be useful for linear optimization problems?}},
url = {http://stacks.iop.org/0266-5611/33/i=4/a=044006?key=crossref.6a47b1c246620584482ca93e603bce1a},
volume = {33},
year = {2017}
}
@article{Censor2015:Eng,
abstract = {Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. H...},
author = {Censor, Yair and Cegielski, Andrzej},
doi = {10.1080/02331934.2014.957701},
file = {:D\:/Mendeley/Censor, Cegielski - 2015 - Projection methods an annotated bibliography of books and reviews.pdf:pdf},
issn = {10294945},
journal = {Optimization},
keywords = {Cimmino,Kaczmarz,annotated bibliography,convex feasibility,fixed points,projection methods,row-action methods,variational inequalities},
language = {english},
number = {11},
pages = {2343--2358},
publisher = {Taylor & Francis},
title = {{Projection methods: an annotated bibliography of books and reviews}},
volume = {64},
year = {2015}
}
@inproceedings{Klee1972:Eng,
address = {New York-London},
author = {Klee, Victor and Minty, George J.},
booktitle = {Inequalities - III. Proceedings of the Third Symposium on Inequalities Held at the University of California, Los Angeles, Sept. 1-9, 1969},
editor = {Shisha, Oved},
file = {:D\:/Mendeley/Klee, Minty - 1972 - How good is the simplex algorithm.pdf:pdf},
keywords = {Linear programming,Simplex method,algorithms complexity},
pages = {159--175},
publisher = {Academic Press},
title = {{How good is the simplex algorithm?}},
year = {1972}
}
@book{Maltsev1970:Rus,
address = {Москва},
author = {Мальцев, Анатолий Иванович},
file = {:D\:/Mendeley/Мальцев - 1970 - Основы линейной алгебры.pdf:pdf},
keywords = {линейная алгебра},
language = {russian},
pages = {402},
publisher = {Наука. Главная редакция физико-математической литературы},
title = {{Основы линейной алгебры}},
year = {1970}
}
@inproceedings{Sokolinskaya2017a,
address = {Челябинск},
author = {Соколинская, Ирина Михайловна and Соколинский, Леонид Борисович},
booktitle = {Параллельные вычислительные технологии (ПаВТ'2017). Короткие статьи и описания плакатов},
file = {:D\:/Mendeley/Соколинская, Соколинский - 2017 - О решении задачи линейного программирования в эпоху больших данных.pdf:pdf},
language = {russian},
pages = {471--484},
publisher = {Издательский центр ЮУрГУ},
title = {{О решении задачи линейного программирования в эпоху больших данных}},
url = {http://omega.sp.susu.ru/pavt2017/short/014.pdf},
year = {2017}
}
@article{Olkhovsky2023a,
abstract = {В статье представлен новый итерационный метод линейного программирования, получивший название “метод поверхностного движения”. Данный метод строит на поверхности многогранника, ограничивающего допустимую область задачи линейного программирования, путь от начальной граничной точки до точки, в которой достигается оптимальное значение целевой функции. Вектор движения строится в направлении максимального увеличения/уменьшения значения целевой функции. Представлено формальное описание алгоритма, реализующего метод поверхностного движения. Доказана теорема сходимости. Описанный метод предполагает использование глубокой нейронной сети прямого распространения для определения направления движения по граням допустимого многогранника. Для этого строится многомер ный локальный образ задачи линейного программирования в точке текущего приближения, который подается на вход нейронной сети. Множество размеченных прецедентов, необходимое для обучения нейронной сети, может быть получено с помощью апекс-метода.},
author = {Ольховский, Николай Александрович and Соколинский, Леонид Борисович},
doi = {10.26089/NumMet.v24r428},
file = {:D\:/Mendeley/Ольховский, Соколинский - 2023 - О новом методе линейного программирования.pdf:pdf},
journal = {Вычислительные методы и программирование},
keywords = {глубокая нейронная сеть,итерационный метод,линейное программирование,метод поверхностного движения,теорема сходимости},
language = {russian},
number = {4},
pages = {408--429},
title = {{О новом методе линейного программирования}},
volume = {24},
year = {2023}
}
@article{Zorkaltsev2018,
author = {Зоркальцев, Валерий Иванович and Мокрый, Игорь Владимирович},
doi = {10.17377/sibjim.2018.21.102},
file = {:D\:/Mendeley/Зоркальцев, Мокрый - 2018 - Алгоритмы внутренних точек в линейной оптимизации.pdf:pdf},
journal = {Сибирский журнал индустриальной математики},
language = {russian},
number = {1 (73)},
pages = {11--20},
title = {{Алгоритмы внутренних точек в линейной оптимизации}},
volume = {21},
year = {2018}
}
