Fukuda, Mituhiro; Kojima, Masakazu Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. (English) Zbl 0979.65051 Comput. Optim. Appl. 19, No. 1, 79-105 (2001). 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. Reviewer: Hang Tong Lau (St.Laurent/Quebec) Cited in 29 Documents 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 Keywords:bilinear matrix inequality eigenvalue problem; semidefinite programming; convex relaxation; cut polytope; branch-and-cut; branch-and-bound; algorithms Software:CSDP; SeDuMi; SDPA; cdd PDFBibTeX XMLCite \textit{M. Fukuda} and \textit{M. Kojima}, Comput. Optim. Appl. 19, No. 1, 79--105 (2001; Zbl 0979.65051) Full Text: DOI