On the Solution of Linear Programming Problems in the Age of Big Data

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 753)

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 \(\varepsilon \)-vicinity of the central point of the cross.

Keywords

NSLP algorithm Non-stationary linear programming problem Large-scale linear programming Fejer mapping 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.South Ural State UniversityChelyabinskRussia

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