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

共 50 条

[1] Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems
V. V. Volkov
V. I. Erokhin
A. S. Krasnikov
A. V. Razumov
M. N. Khvostov
Computational Mathematics and Mathematical Physics, 2017, 57 : 1757 - 1770
[2] Matrix correction of a dual pair of improper linear programming problems
Erokhin V.I.
Computational Mathematics and Mathematical Physics, 2007, 47 (4) : 564 - 578
[3] Matrix Correction of a Dual Pair of Improper Linear Programming Problems with a Block Structure
Erokhin, V. I.
Krasnikov, A. S.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2008, 48 (01) : 76 - 84
[4] Matrix correction of a dual pair of improper linear programming problems with a block structure
V. I. Erokhin
A. S. Krasnikov
Computational Mathematics and Mathematical Physics, 2008, 48 : 76 - 84
[5] Matrix corrections minimal with respect to the Euclidean norm for linear programming problems
Erokhin, V. I.
Krasnikov, A. S.
Khvostov, M. N.
AUTOMATION AND REMOTE CONTROL, 2012, 73 (02) : 219 - 231
[6] Matrix corrections minimal with respect to the Euclidean norm for linear programming problems
V. I. Erokhin
A. S. Krasnikov
M. N. Khvostov
Automation and Remote Control, 2012, 73 : 219 - 231
[7] APPROXIMATION OF NON-EIGEN PROBLEMS OF LINEAR-PROGRAMMING USING THE EUCLIDEAN NORM CRITERION
VATOLIN, AA
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1984, 24 (06): : 200 - 201
[8] CONTINUOUS ALGORITHM FOR SOLVING DUAL PAIR OF LINEAR-PROGRAMMING PROBLEMS
KARPINSKAYA, NN
AUTOMATION AND REMOTE CONTROL, 1977, 38 (07) : 1106 - 1112
[9] On the parallel use of the decomposition method in a pair of dual problems of linear programming
Mednitskii, YV
JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL, 1998, 37 (01) : 102 - 106
[10] MINIMUM NORM SOLUTIONS TO LINEAR ELASTIC ANALYSIS PROBLEMS
KANEKO, I
PLEMMONS, RJ
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1984, 20 (06) : 983 - 998

← 1 2 3 4 5 →