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On a structured semidefinite program. (English) Zbl 1234.90010

Summary: The nonnegative biquadratics discussed comes from the Böttcher-Wenzel inequality. It is for some matrices a sum of squares of polynomials (SOS), in other cases not, depending on the nonzero pattern of the matrices at issue. Our aim was to draw a line between them. To prove the ‘not a SOS’ case we solve a semidefinite programming (SDP) problem. Subsequently a two-parameter version will be investigated.

MSC:

90C22 Semidefinite programming
15A45 Miscellaneous inequalities involving matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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