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Article Dans Une Revue Mathematical Programming, Series A Année : 2014

New approximations for the cone of copositive matrices and its dual

Résumé

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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Dates et versions

hal-00545755 , version 1 (12-12-2010)
hal-00545755 , version 2 (19-01-2012)

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Jean-Bernard Lasserre. New approximations for the cone of copositive matrices and its dual. Mathematical Programming, Series A, 2014, 144, pp.265-276. ⟨10.1007/s10107-013-0632-5⟩. ⟨hal-00545755v2⟩
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