A Global BMI Algorithm Based on the Generalized Benders Decomposition

E. Beran, L. Vandenberghe, and S. Boyd

Proceedings of the European Control Conference, paper no.934, 1997.

We present a new algorithm for the global solution of optimization problems involving bilinear matrix inequalities (BMIs). The method is based on a technique known in large-scale and global optimization as the generalized Benders decomposition. It extends the efficient GOP algorithm of Visweswaran and Floudas for bilinear and biconvex programming to problems with BMI constraints.