Linear interval tolerance problem and linear programming techniques
type: Item
instance of: scholarly article
title: Linear interval tolerance problem and linear programming techniques
zbMATH Open document ID: 1003.65061
DOI: 10.1023/A:1014758201565
author: Bernard Philippe
author: Olivier Beaumont
published in: Reliable Computing
publication date: 2002-05-30T00:00:00Z
review text: Let \([A]x= [b]\) be an \(n\)-dimensional system of linear interval equations. Then \(\Sigma_{\forall\exists}\) denotes the set of all \(x\in\mathbb{R}^n\) such that to any \(A\in [A]\) there exists a \(b\in [b]\) with \(Ax= b\). Two different subsets, \(S_1\) and \(S_2\) of \(\Sigma_{\forall\exists}\) which were defined by \textit{J. Rohn} [Lect. Notes Comput. Sci. 212, 157-158 (1986; Zbl 0588.65024)] are rewritten. Then the simplex algorithm together with an appropriate cost function is applied to find optimal interval vectors which are contained in \(S_1\) or \(S_2\).
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 1747909
zbMATH Keywords: linear interval tolerance problem
zbMATH Keywords: linear programming
zbMATH Keywords: system of linear interval equations
zbMATH Keywords: simplex algorithm
zbMATH Keywords: optimal interval vectors
reviewed by: H. Ratschek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1747909