Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and thei...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 175; no. 1; pp. 76 - 103
Main Authors: Kostyukova, Olga, Tchemisova, Tatiana
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2017
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Economic models
Engineering
Inequalities
Mathematics
Mathematics and Statistics
Nonlinear analysis
Nonlinear programming
Operations Research/Decision Theory
Optimization
Proving
Theory of Computation
Optimality conditions
Convex set
90C30
90C25
Immobile index
90C34
Finitely representable set
Constraint qualifications (CQ)
Convex programming
Nonlinear programming (NLP)
Semi-infinite programming (SIP)
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1150-z