Computable bounds on parametric solutions of convex problems
type: Item
instance of: scholarly article
title: Computable bounds on parametric solutions of convex problems
zbMATH Open document ID: 0649.90081
DOI: 10.1007/BF01580732
author: Anthony V. Fiacco
author: Jerzy Kyparisis
published in: Mathematical Programming. Series A. Series B
publication date: 1988-01-01T00:00:00Z
review text: For the parametric convex problem \(\min_{x}f(x,\epsilon)\), such that \(x\in R(\epsilon)\), where \(R(\epsilon)=\{x\in E^ n;\) \(g_ i(x,\epsilon)\geq 0\), \(i=1,...,m\), \(h_ j(x,\epsilon)=0\), \(j=1,...,p\}\), \(\epsilon\in E^ r\) is the vector of parameters, \(f: E^ n\times E^ r\to E^ 1\) is \(C^ 2\) and convex in \((x,\epsilon)\), \(g_ i: E^ n\times E^ r\to E^ 1\) are \(C^ 2\) and concave in \((x,\epsilon)\) and \(h_ j: E^ n\times E^ r\to E^ 1\) are affine in \((x,\epsilon)\), the authors obtain computable upper and lower bounds on the optimal solution.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4061002
zbMATH Keywords: parametric convex problem
zbMATH Keywords: upper and lower bounds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4061002