Facial reduction in partially finite convex programming
type: Item
instance of: scholarly article
title: Facial reduction in partially finite convex programming
zbMATH Open document ID: 0828.90136
DOI: 10.1007/BF01581693
published in: Mathematical Programming. Series A. Series B
publication date: 1994-09-26T00:00:00Z
review text: The problem \(f(x)\to \inf\) subject to \(Ax- b\in K\) is considered where \(f\) is an convex functional on an infinite-dimensional locally convex topological vector space \(X\), \(A\) is a linear operator from \(X\) to \(\mathbb{R}^n\) and \(K\) is a closed convex cone of \(\mathbb{R}^n\). For necessary conditions of optimality constraint qualifications are usually required. If these regularity conditions fail reduction techniques due to the description of the feasible region are useful [cf. A. Ben Israel, A. Ben-Tal, S. Zlobec (1981)]. In this paper a facial reduction in the domain space is used maintaining the involved structure. Using the quasi- relative interior instead of the relative interior of a convex set the achieved results are similar to the known ones in finite dimensions. Some applications to constrained approximation problems in separable \(L_p(S, \mu)\) spaces are given.
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 52A41
zbMATH DE Number: 644752
zbMATH Keywords: partially finite convex programming
zbMATH Keywords: infinite-dimensional locally convex topological vector space
zbMATH Keywords: regularity conditions
zbMATH Keywords: facial reduction
zbMATH Keywords: constrained approximation
author: A. S. Lewis
reviewed by: Armin Hoffmann
MaRDI profile type: Publication
cites work: Q3902815
cites work: Duality Relationships for Entropy-Like Minimization Problems
cites work: Partially finite convex programming. I: Quasi relative interiors and duality theory
cites work: Partially finite convex programming. II: Explicit lattice models
cites work: Partially-Finite Programming in $L_1 $ and the Existence of Maximum Entropy Estimates
cites work: Strong Rotundity and Optimization
cites work: Q3916398
cites work: A simple constraint qualification in infinite dimensional programming
cites work: Q4747150
cites work: Constrained best approximation in Hilbert space
cites work: Constrained best approximation in Hilbert space. II
cites work: Dual Methods in Entropy Maximization. Application to Some Problems in Crystallography
cites work: Q4104377
cites work: Extremal structure of convex sets. II
cites work: Constrained \(L_ p\) approximation
cites work: Integrals which are convex functionals
cites work: Convex Analysis
cites work: Q5516901
cites work: Q4049667
full work available at URL: https://doi.org/10.1007/bf01581693
OpenAlex ID: W2133667750
description: scientific article; zbMATH DE number 644752