BMI global optimization based on branch and bound method taking account of the property of local minima

This paper deals with the global optimization of the BMI (bilinear matrix inequalities) eigenvalue problem. At first, we clarify some geometric properties of local minima of the BMI optimization problem. Then, based on these results, we give a modified branch and bound method for the BMI global optimization which improves the numerical efficiency, and demonstrate its optimization process by a simple numerical example.