Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems

被引：5

作者：

Volkov, V. V. ^{[1
]}

Erokhin, V. I. ^{[2
]}

Krasnikov, A. S. ^{[3
]}

Razumov, A. V. ^{[2
]}

Khvostov, M. N. ^{[1
]}

机构：

[1] Voronezh State Univ, Borisoglebsk Branch, Borisoglebsk 397160, Voronezh Oblast, Russia

[2] Mozhaisky Mil Space Acad, St Petersburg 197198, Russia

[3] Russia State Social Univ, Moscow 129226, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2017年 / 57卷 / 11期

基金：

俄罗斯基础研究基金会;

关键词：

dual pair of linear programming problems; improper linear programming problems; inverse linear programming problems; minimal matrix correction; Euclidean norm; SYSTEMS; EQUATIONS;

D O I：

10.1134/S0965542517110148

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a pair of dual (possibly improper) linear programming problems, a family of matrix corrections is studied that ensure the existence of given solutions to these problems. The case of correcting the coefficient matrix and three cases of correcting an augmented coefficient matrix (obtained by adding the right-hand side vector of the primal problem, the right-hand-side vector of the dual problem, or both vectors) are considered. Necessary and sufficient conditions for the existence of a solution to the indicated problems, its uniqueness is proved, and the form of matrices for the solution with a minimum Euclidean norm is presented. Numerical examples are given.

引用

页码：1757 / 1770

页数：14

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