201 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
Extremal copositive matrices with minimal zero supports of cardinality two
Let be an extremal copositive matrix with unit diagonal.
Then the minimal zeros of all have supports of cardinality two if and only
if the elements of are all from the set . Thus the extremal
copositive matrices with minimal zero supports of cardinality two are exactly
those matrices which can be obtained by diagonal scaling from the extremal
unit diagonal matrices characterized by Hoffman and Pereira in
1973.Comment: 4 page
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