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 Study of a special nonlinear problem arising in convex semi-infinite programming
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6190

title: Study of a special nonlinear problem arising in convex semi-infinite programming
authors: Kostyukova, O.
Tchemisova, T.
Yermalinskaya, S.
issue date: 2009
publisher: Springer Verlag
abstract: We consider convex problems of semi-infinite programming (SIP) using an approach based on the implicit optimality criterion. This criterion allows one to replace optimality conditions for a feasible solution x0 of the convex SIP problem by such conditions for x0 in some nonlinear programming (NLP) problem denoted by NLP(I(x0)). This nonlinear problem, constructed on the base of special characteristics of the original SIP problem, so-called immobile indices and their immobility orders, has a special structure and a diversity of important properties. We study these properties and use them to obtain efficient explicit optimality conditions for the problem NLP(I(x0)). Application of these conditions, together with the implicit optimality criterion, gives new efficient optimality conditions for convex SIP problems. Special attention is paid to SIP problems whose constraints do not satisfy the Slater condition and to problems with analytic constraint functions for which we obtain optimality conditions in the form of a criterion. Comparison with some known optimality conditions for convex SIP is provided.
URI: http://hdl.handle.net/10773/6190
ISSN: 1072-3374
publisher version/DOI: http://dx.doi.org/10.1007/s10958-009-9608-7
source: Journal of Mathematical Sciences
appears in collectionsCIDMA - Artigos

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