The inverse problem for standard linear programming problems
type: Item
instance of: scholarly article
title: The inverse problem for standard linear programming problems
zbMATH Open document ID: 0970.90051
author: S. M. Shvartin
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The inverse problem for standard linear programming ones (SLPP) is solved. More exactly, fix a (matrix) triplet \((A,b,C)\) of the coefficients which determines a SLPP, and suppose that the corresponding canonical problem has a nondegenerate support optimal solution \(X_0\in \mathbb{R}^{n+m}\). The problem is to find the set of all canonical problems such that the first \(n\) coordinates of their nondegenerate basis optimal solutions equal the corresponding coordinates of \(X_0\). Three cases are considered depending on the structure (the number of positive coordinates) of the optimal solution \(X_0\). For each case the desired set (that equals the set of all SLPP with the optimal solution) is constructed in the explicit form and is parametrized by the given coefficients.
reviewed by: Evsei Morozov
Mathematics Subject Classification ID: 90C08
zbMATH DE Number: 1557727
zbMATH Keywords: standard linear programming problem
zbMATH Keywords: inverse problem
zbMATH Keywords: optimal solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557727