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Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. (English) Zbl 0979.65051

The authors propose new branch-and-bound and branch-and-cut algorithms to solve the bilinear matrix inequality eigenvalue problem. Numerical results on large randomly generated test problems are presented to compare between the new algorithm and some previously known algorithms.

MSC:

65K05 Numerical mathematical programming methods
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C22 Semidefinite programming
90C25 Convex programming
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

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