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Title: CQ-free optimality conditions and strong dual formulations for a special conic optimization problem
Author: Kostyukova, Olga
Tchemisova, Tatiana
Keywords: Conic optimization
Set-semidefinite optimization
Optimality conditions
Normalized immobile index set
Regularized dual problem
Strong duality
Issue Date: 2020
Publisher: International Academic Press
Abstract: In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite (orK-semidefinite) programming problems, where the setKis a polyhedral convex cone. For these problems, we introduce theconcept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. Thisstudy provides the main result of the paper, which is to formulate and prove the new first-order optimality conditions inthe form of a criterion. The optimality conditions are explicit and do not use any constraint qualifications. For the case of alinear cost function, we reformulate theK-semidefinite problem in a regularized form and construct its dual. We show thatthe pair of the primal and dual regularized problems satisfies the strong duality relation which means that the duality gap is vanishing.
Peer review: yes
DOI: 10.19139/soic-2310-5070-915
ISSN: 2311-004X
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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