Optimal solution characterization for infinite positive semi-definite programming
type: Item
instance of: scholarly article
title: Optimal solution characterization for infinite positive semi-definite programming
zbMATH Open document ID: 0809.49033
DOI: 10.1016/0893-9659(94)90013-2
author: V. Pereyra
published in: Applied Mathematics Letters
publication date: 1994-09-22T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/31452
review text: Let (P) denote the general convex programming problem: \[ \text{minimize } C(x)\text{ subject to } x\in X, \] where \(X\) is a nonempty, closed, convex subset of a real Hilbert space \(H\) and \(C\) is a convex, real-valued function on \(H\). Let \(X^*\) denote the set of optimal solutions of (P). The objective is to find additional assumptions on the convex objective function \(C\) which are sufficient to conclude that \(X^*\) is affine whenever \(X\) is. To this end suppose \(C(x)= 1/2\langle x,Q(x)\rangle+ \langle x,c\rangle\) for \(x\in H\), where \(Q: H\to H\) is a bounded linear operator on \(H\) and \(c\in H\). (P) is thus transformed into a quadratic programming problem (P\('\)). The result presented in this paper is the following: If \(Q\) in (P\('\)) is positive semidefinite, and if \(X\) is affine in \(H\), then the set of optimal solutions of (P\('\)), \(X^*\), is also affine in \(H\).
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C34
zbMATH DE Number: 643822
zbMATH Keywords: infinite positive semi-definite programming
zbMATH Keywords: quadratic programming
reviewed by: Reinhardt Euler
MaRDI profile type: Publication
OpenAlex ID: W2016008174
cites work: On the Control of Discrete-Time Distributed Parameter Systems
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cites work: Q5601627
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description: scientific article; zbMATH DE number 643822