Convex semi-infinite programming: Implicit optimality criterion based on the concept of immobile indices
type: Item
instance of: scholarly article
title: Convex semi-infinite programming: Implicit optimality criterion based on the concept of immobile indices
zbMATH Open document ID: 1203.90165
author: O. I. Kostyukova
author: S. A. Yermalinskaya
author: Tatiana V. Tchemisova
published in: Journal of Optimization Theory and Applications
publication date: 2010-08-13T00:00:00Z
review text: The paper of O. I. Kostyukova, T. V. Tchemisova and S. A. Yermalinskayais is located in the area of semi-infinite programming (SIP) which stands in between the classical optimization (with a finite number of (equality and) inequality constraints) and infinite programming (where the optimization takes place in an infinite dimensional space). In fact, in SIP, an infinite number of inequality constraints may occur. Motivations of SIP come, among many other fields, from Chebychev approximation, maneuverability of robots, optimal control, modeling of genetic networks and special cases of infinite kernel learning. Researchers in SIP could develop various concepts of algorithms by the locally approximation (or even representation) of their progam with a much smaller (in fact, finite) number of inequality constraints. The authors contribute to this tradition under the assumption of (in the state variable) convex model functions and by the help of the concept of ``immobility''. The authors state a new implicit optimality criterion for convex semi-infinite programming (SIP) problems. That criterion does not require any constraint qualification but, indeed, it bases on the concept of immobile index and immobility order. For any given convex SIP program with a continuum of constraints, the authors use an information about its immobile indices to construct a nonlinear programming (NLP) problem of some special form. They prove that a feasible point of the original (infinitely constrained) SIP problem is optimal if and only if it is optimal in the corresponding (finitely constrained) NLP problem. With the help of optimality theory of NLP, the previous fact allows the authors to obtain new efficient optimality conditions for convex SIP problems. To construct the NLP problem, the authors use the DIO algorithm. They provide a comparison of their optimality conditions with known results. This article is well written, structured and, by proofs and examples, demonstrated; it advances gi…
reviewed by: Gerhard-Wilhelm Weber
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5770310
zbMATH Keywords: convex semi-infinite programming
zbMATH Keywords: nonlinear programming
zbMATH Keywords: optimality criteria
zbMATH Keywords: constraint qualifications
MaRDI profile type: Publication
full work available at URL: s10957-009-9621-5
OpenAlex ID: W2073875740
Wikidata QID: Q57677651
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DOI: 10.1007/S10957-009-9621-5
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description: scientific article; zbMATH DE number 5770310