An estimate of the convergence rate for the linear programming quasisolution method
type: Item
instance of: scholarly article
title: An estimate of the convergence rate for the linear programming quasisolution method
zbMATH Open document ID: 0733.90045
author: F. P. Vasil'ev
published in: Moscow University Computational Mathematics and Cybernetics
publication date: 1991-01-01T00:00:00Z
review text: The author considers the linear programming problem \(f(x)=<c,x>\to \inf\), \(x\in X\), where X is a polyhedron described by \(X=(x\in R^ n_+:\) \(<a_ i,x>\leq b_ i\), \(i=1,...,m\); \(<a_ i,x>=b_ i\), \(i=m+1,...,s).\) When instead of the data c, \(a_ i\) and \(b_ i\), \(i=1,2,...,s\), some approximations are given, then the problem may become unstable in general. Therefore the linear programming problem must first be regularized. Such a regularization method of the quasisolutions is proposed. The stabilizing function chosen in the article is \(\Omega (x)=x_ 1+x_ 2+...+x_ n\), \(x\in R^ n_+\).
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4213736
zbMATH Keywords: estimation of the convergence rate
zbMATH Keywords: regularization method
zbMATH Keywords: quasisolutions
zbMATH Keywords: stabilizing function
reviewed by: Maxim Ivanov Todorov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4213736