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arXiv · 1012.2552

New approximations for the cone of copositive matrices and its dual

Jean Bernard Lasserre
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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 the 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.

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Jean Bernard Lasserre. 2010-12-12. New approximations for the cone of copositive matrices and its dual. https://arxiv.org/abs/1012.2552

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