Smoothing by mollifiers. I: Semi-infinite optimization
type: Item
instance of: scholarly article
title: Smoothing by mollifiers. I: Semi-infinite optimization
zbMATH Open document ID: 1166.90017
author: Hubertus T. Jongen
author: Oliver Stein
published in: Journal of Global Optimization
publication date: 2008-07-30T00:00:00Z
review text: The authors study the standard semi-infinite programming problem where the index set is described by finitely many inequality constraints and all functions involved are twice continuously differentiable. They begin with a summary of the essential definitions and properties respectively of the feasible set, the lower level problem, regularity, stationarity, the Reduction Ansatz, and so-called mollifiers. Then they prove that, under some regularity assumptions, the nonempty compact feasible set of the problem can be approximated arbitrary well by a level set of a single smooth function which is constructed as the mollification of the optimal value function of the lower level problem. Next correspondences are shown between the Karush-Kuhn-Tucker points of the original and the smooth finite optimization problem defined via the approximated feasible set, and a result concerning the associated Morse indices is presented. The latter result, which is proved in part II of the paper (appearing in J. Glob. Optimiz.), finally enables the prove of the connectedness of the so-called min-max digraph for semi-infinite programming problems.
reviewed by: Rembert Reemtsen
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 57R12
zbMATH DE Number: 5306197
zbMATH Keywords: semi-infinite programming
zbMATH Keywords: smoothing
zbMATH Keywords: mollifier
zbMATH Keywords: stationarity
zbMATH Keywords: lower level problem
zbMATH Keywords: morse index
MaRDI profile type: Publication
full work available at URL: s10898-007-9232-3
OpenAlex ID: W2071920504
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DOI: 10.1007/S10898-007-9232-3
description: scientific article; zbMATH DE number 5306197