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 Convex semi-infinite programming: Implicit optimality criterion based on the concept of immobile indices
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6188

title: Convex semi-infinite programming: Implicit optimality criterion based on the concept of immobile indices
authors: Kostyukova, O. I.
Tchemisova, T. V.
Yermalinskaya, S. A.
keywords: Convex semi-infinite programming
Nonlinear programming
Optimality criteria
Constraint qualifications
issue date: 2010
publisher: Springer Verlag
abstract: We state a new implicit optimality criterion for convex semi-infinite programming (SIP) problems. This criterion does not require any constraint qualification and is based on concepts of immobile index and immobility order. Given a convex SIP problem with a continuum of constraints, we use an information about its immobile indices to construct a nonlinear programming (NLP) problem of a special form. We prove that a feasible point of the original infinite SIP problem is optimal if and only if it is optimal in the corresponding finite NLP problem. This fact allows us to obtain new efficient optimality conditions for convex SIP problems using known results of the optimality theory of NLP. To construct the NLP problem, we use the DIO algorithm. A comparison of the optimality conditions obtained in the paper with known results is provided.
URI: http://hdl.handle.net/10773/6188
ISSN: 0022-3239
publisher version/DOI: http://dx.doi.org/10.1007/s10957-009-9621-5
source: Journal of Optimization Theory and Applications
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