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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2016

Considering copositivity locally

Résumé

We say that a symmetric matrix A is copositive if v^TAv ≥ 0 for all nonnegative vectors v. The main result of this paper is a characterization of the cone of feasible directions at a copositive matrix A, i.e., the convex cone of symmetric matrices B such that there exists δ>0 satisfying A+δB being copositive. This cone is described by a set of linear inequalities on the elements of B constructed from the so called set of (minimal) zeros of A. This characterization is used to furnish descriptions of the minimal (exposed) face of the copositive cone containing A in a similar manner. In particular, we can check whether A lies on an extreme ray of the copositive cone by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sufficient condition for the irreducibility of A with respect to a copositive matrix C.

Dates et versions

hal-01417510 , version 1 (15-12-2016)

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Peter J. C. Dickinson, Roland Hildebrand. Considering copositivity locally. Journal of Mathematical Analysis and Applications, 2016, 437 (2), pp.1184-1195. ⟨10.1016/j.jmaa.2016.01.063⟩. ⟨hal-01417510⟩
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