805 research outputs found
New approximations for the cone of copositive matrices and its dual
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.Comment: 8
An algorithm for determining copositive matrices
In this paper, we present an algorithm of simple exponential growth called
COPOMATRIX for determining the copositivity of a real symmetric matrix. The
core of this algorithm is a decomposition theorem, which is used to deal with
simplicial subdivision of on
the standard simplex , where each component of the vector is
-1, 0 or 1.Comment: 15 page
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