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

Olga Kostyukova () and Tatiana Tchemisova ()
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Olga Kostyukova: National Academy of Sciences of Belarus
Tatiana Tchemisova: University of Aveiro

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 1, No 4, 76-103

Abstract: Abstract 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.

Keywords: Convex programming; Semi-infinite programming (SIP); Nonlinear programming (NLP); Convex set; Finitely representable set; Constraint qualifications (CQ); Immobile index; Optimality conditions; 90C25; 90C30; 90C34 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-017-1150-z

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