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Copositivity detection by difference-of-convex decomposition and omega-subdivision

Immanuel M. Bomze (immanuel.bomze***at***univie.ac.at)
Gabriele Eichfelder (Gabriele.Eichfelder***at***tu-ilmenau.de)

Abstract: We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of $\omega$-subdivision type. The tests employ LP or convex QP techniques, but also can be used heuristically using appropriate test points. We also discuss the selection of efficient d.c.~decompositions and propose some preprocessing ideas based on the spectral d.c.~decomposition. We report on first numerical experience with this procedure which are very promising.

Keywords: copositive programming

Category 1: Linear, Cone and Semidefinite Programming (Other )

Citation: AM Preprint Series No. 333, Univ. Erlangen-Nuremberg; and Technical Report 2011-05, ISOR, Univ. Wien. To appear in: Math. Programming A

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Entry Submitted: 01/14/2010
Entry Accepted: 01/14/2010
Entry Last Modified: 04/22/2012

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