Convex Semi-Infinite Programming: Implicit Optimality Criterion Based on the Concept of Immobile Indices

O. I. Kostyukova (), T. V. Tchemisova () and S. A. Yermalinskaya ()
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O. I. Kostyukova: Institute of Mathematics, National Academy of Sciences of Belarus
T. V. Tchemisova: University of Aveiro
S. A. Yermalinskaya: Belorussian State University of Informatics and Radio-electronics

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 2, No 7, 325-342

Abstract: 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.

Keywords: Convex semi-infinite programming; Nonlinear programming; Optimality criteria; Constraint qualifications (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-009-9621-5

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