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http://hdl.handle.net/10773/30240
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 |
URI: | http://hdl.handle.net/10773/30240 |
DOI: | 10.19139/soic-2310-5070-915 |
ISSN: | 2311-004X |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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915-Article Text-4545-4-10-20200806.pdf | 169.84 kB | Adobe PDF | View/Open |
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