Necessary conditions for upper semicontinuity in parametric semi-infinite programming
type: Item
instance of: scholarly article
title: Necessary conditions for upper semicontinuity in parametric semi-infinite programming
zbMATH Open document ID: 0556.90087
DOI: 10.1007/BF00938590
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: We treat semi-infinite optimization problems: Minimize p(x) subject to \(x\in {\mathbb{R}}^ m\), and a(t,x)\(\leq b(t)\) for all \(t\in T\), where T is a \(\sigma\)-compact topological space, and p, a, b are suitable (- \(\infty,\infty)\)-valued functions on \({\mathbb{R}}^ m\), respectively. Linear, convex, and quasi-convex semi-infinite programming are included in this concept. The main results of this paper are on the necessity of the compactness of the set of feasible points for (a,b), and the set of \(\phi\)-optimal solutions for (p,a,b) for the (Hausdorff) upper semicontinuity of the feasible set-mapping in (a,b), and the \(\phi\)- optimal solution-mapping in (p,a,b), respectively (where the parameter sets are provided with a suitable topology). Some more special results complete the paper.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 3887465
zbMATH Keywords: parametric programming
zbMATH Keywords: set-valued mappings
zbMATH Keywords: semi-infinite optimization
zbMATH Keywords: upper semicontinuity
zbMATH Keywords: feasible set
author: Rainer Colgen
MaRDI profile type: Publication
cites work: Q3968041
cites work: Metric characterizations of upper semicontinuity
cites work: A characterization of semicontinuity-preserving multifunctions
cites work: Continuity properties in semi-infinite parametric linear optimization
cites work: Q5547252
description: scientific article; zbMATH DE number 3887465