On the Solution of Linear Programming Problems in the Age of Big Data
The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are non-stationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary linear programming problems on modern cluster computing systems....
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| Published in | Parallel Computational Technologies Vol. 753; pp. 86 - 100 |
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| Main Authors | , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2017
Springer International Publishing |
| Series | Communications in Computer and Information Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783319670348 3319670344 |
| ISSN | 1865-0929 1865-0937 |
| DOI | 10.1007/978-3-319-67035-5_7 |
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| Summary: | The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are non-stationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary linear programming problems on modern cluster computing systems. The algorithm consists of two phases: Quest and Targeting. The Quest phase calculates a solution of the system of inequalities defining the constraint system of the linear programming problem under the condition of dynamic changes in input data. To this end, the apparatus of Fejer mappings is used. The Targeting phase forms a special system of points having the shape of an n-dimensional axisymmetric cross. The cross moves in the n-dimensional space in such a way that the solution of the linear programming problem is located all the time in an $$\varepsilon $$ -vicinity of the central point of the cross. |
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| Bibliography: | Original Abstract: The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are non-stationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary linear programming problems on modern cluster computing systems. The algorithm consists of two phases: Quest and Targeting. The Quest phase calculates a solution of the system of inequalities defining the constraint system of the linear programming problem under the condition of dynamic changes in input data. To this end, the apparatus of Fejer mappings is used. The Targeting phase forms a special system of points having the shape of an n-dimensional axisymmetric cross. The cross moves in the n-dimensional space in such a way that the solution of the linear programming problem is located all the time in an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-vicinity of the central point of the cross. The reported study has been partially supported by the RFBR according to research project No. 17-07-00352-a, by the Government of the Russian Federation according to Act 211 (contract No. 02.A03.21.0011) and by the Ministry of Education and Science of the Russian Federation (government order 2.7905.2017/8.9). |
| ISBN: | 9783319670348 3319670344 |
| ISSN: | 1865-0929 1865-0937 |
| DOI: | 10.1007/978-3-319-67035-5_7 |