Strong duality for infinite-dimensional vector-valued programming problems
type: Item
instance of: scholarly article
title: Strong duality for infinite-dimensional vector-valued programming problems
zbMATH Open document ID: 0654.90098
DOI: 10.1007/BF00939816
author: S. H. Smith
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let X, Y, and Z be locally convex real topological vector spaces, \(A\subset X\) a convex subset, and let \(C\subset Y\), \(E\subset Z\) be cones. Let f: \(X\to Z\) be E-concave and g: \(X\to Y\) be C-concave functions. We consider a concave programming problem with respect to an abstract cone and its strong dual problem as follows: \[ (P)\quad \max imize\quad f(x),\quad subject\quad to\quad x\in A,\quad g(x)\in C, \] \[ (SD)\quad \min imize\quad \{\cup_{\phi \in C\quad +}\max \{(f+\phi \circ g)(A):\quad E\}\}, \] where C \(+\) denotes the set of all nonnegative continuous linear operators from Y to Z and (SD) is the strong dual problem to (P). The authors find a necessary condition of strong saddle point for Problem (P) and establish the strong duality relationships between Problems (P) and (SD).
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 4068652
zbMATH Keywords: cone concavity
zbMATH Keywords: strong maximal points
zbMATH Keywords: pseudo tangent cones
zbMATH Keywords: locally convex real topological vector spaces
zbMATH Keywords: cones
zbMATH Keywords: concave programming
zbMATH Keywords: strong dual
zbMATH Keywords: nonnegative continuous linear operators
zbMATH Keywords: necessary condition of strong saddle point
reviewed by: Hang-Chin Lai
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4068652