Characterizations of optimal solution sets of convex infinite programs
type: Item
instance of: scholarly article
title: Characterizations of optimal solution sets of convex infinite programs
zbMATH Open document ID: 1201.90158
author: J. Martínez
published in: Top
publication date: 2009-06-17T00:00:00Z
review text: The authors consider the convex infinite optimization problem \[ \operatorname{Min} f(x) \;\text{ s.t }\;f_t(x) \leq 0,\;\forall t\in T \text{ and }x \in C, \tag{P} \] where \(X\) is a locally convex Hausdorff topological vector space, \(f\), \(f_t: X \rightarrow\mathbb R \cup (+\infty)\), \(t \in T\), are proper, lower semi-continuous and convex functions, \(C\) is a nonempty, closed convex subset of \(X\), and \(T\) is an arbitrary index set. Several characterizations of the solution set of (P) are given together with the characterization of the solution set of (P) when a minimizing sequence (instead of a solution of (P)) is known. These results are also obtained for cone-constrained convex programs. They also obtain optimality condition for a semi-convex program with convex constraints and give characterizations of its solution set.
reviewed by: R. N. Kaul
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5565942
zbMATH Keywords: convex infinite programs
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: solutions sets
zbMATH Keywords: semi-convex programs
MaRDI profile type: Publication
full work available at URL: s11750-008-0039-2
OpenAlex ID: W1979563734
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DOI: 10.1007/S11750-008-0039-2
description: scientific article; zbMATH DE number 5565942