Solving the Problem of Linear Programming on the Basis of Multiplex Approach

Mikhail M. Lychak; Vladimir N. Shevchenko; Nina P. Tsaruk

doi:10.1615/J Automat Inf Scien.v37.i8.30

Journal of Automation and Information Sciences

Editor-in-Chief: Arkadiy A. Chikriy (open in a new tab)

Associate Editors: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

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Solving the Problem of Linear Programming on the Basis of Multiplex Approach

Volume 37, Issue 8, 2005, pp. 26-33

DOI: 10.1615/J Automat Inf Scien.v37.i8.30

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Mikhail M. Lychak
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kyiv, Ukraine

Vladimir N. Shevchenko
Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Kiev

Nina P. Tsaruk
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kiev, Ukraine

ABSTRACT

A technique of solving linear programming (LP) problem on a set of arguments is suggested. The set is prescribed by a system of linear inequalities. The technique uses construction of a finite sequence of simplified estimates in the form of cones by goal-oriented adjunction and rejection of corresponding half-spaces. An iterative algorithm of enumerating of constraints, which are adjuncted, is substantiated and derived. A new software module for solving LP problem in MATLAB environment is created. Its comparison with a standard MATLAB function (linprog) demonstrated significant advantages both in quick-action (not less, than eight times faster) and in possibility of solving large-dimension LP problems (more, than one hundred variables).

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