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|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|
|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.|
|publisher version/DOI: ||http://dx.doi.org/10.1007/s10957-009-9621-5|
|source: ||Journal of Optimization Theory and Applications|
|appears in collections||CIDMA - Artigos|
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