On equivalent representations and properties of faces of the cone of copositive matrices. (2nd November 2022)

• Record Type: Journal Article
• Authors: Kostyukova, O. I.; Tchemisova, T. V.
• Is Part Of: Optimization. Volume 71:Number 11(2022)
• Page Start: 3211
• Page End: 3239
• Publication Date: 2022-11-02
• Subjects: Copositive programming -- zero vectors of a subset of copositive matrices -- regularization -- face reduction -- the Slater condition; 49N15 -- 90C25 -- 90C34 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2027939
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The paper is devoted to the study of the cone C O P p of copositive matrices. Based on the concept of immobile indices known from semi-infinite optimization, we define zero and minimal zero vectors of a subset of the cone C O P p and use them to obtain different representations of the faces of C O P p and the corresponding dual cones. The minimal face of C O P p containing a given convex subset of this cone is described, and some propositions are proved that allow obtaining equivalent descriptions of the feasible sets of copositive problems.