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New approximations for the cone of copositive matrices and its dual

Jean B. Lasserre(lasserre***at***laas.fr)

Abstract: We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C (resp. for its dual), thus complementing previous inner (resp. outer) approximations for C (for its dual). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to K-copositivity and K-complete positivity for a closed convex cone K, is straightforward.

Keywords: copositive matrices; completely positive matrices; semidefinite relaxations

Category 1: Linear, Cone and Semidefinite Programming


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Entry Submitted: 12/11/2010
Entry Accepted: 12/11/2010
Entry Last Modified: 12/11/2010

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