New approximations for the cone of copositive matrices and its dual

Details New approximations for the cone of copositive matrices and its dual New approximations for the cone of copositive matrices and its dual

2010-12-12

arxiv.org/abs/1012.2552v2

Mathematics

Optimization and Control

8p

Scientific paper

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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