Set intersection theorems and existence of optimal solutions
type: Item
instance of: scholarly article
title: Set intersection theorems and existence of optimal solutions
zbMATH Open document ID: 1133.90009
author: Dimitri P. Bertsekas
author: Paul Tseng
published in: Mathematical Programming. Series A. Series B
publication date: 2007-05-10T00:00:00Z
review text: In this interesting paper one establishes sufficient conditions for a decreasing sequence of closed subsets of \(\mathbb{R}^{n}\) to have nonempty intersection. The conditions are formulated in terms of asymptotic directions, retractive directions and horizon directions. In order to apply the results to the existence of global solutions for constrained minimization problems one introduces the notion of bidirectionally flat convex functions. One recovers so the Frank-Wolfe theorem.
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C47
zbMATH DE Number: 5151338
zbMATH Keywords: set intersection
zbMATH Keywords: asymptotic direction
zbMATH Keywords: recession direction
zbMATH Keywords: global minimum
zbMATH Keywords: Frank-Wolfe theorem
zbMATH Keywords: quasiconvex function
reviewed by: Constantin Zălinescu
MaRDI profile type: Publication
full work available at URL: s10107-006-0003-6
OpenAlex ID: W2021872351
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DOI: 10.1007/S10107-006-0003-6
description: scientific article; zbMATH DE number 5151338