A Randomized Algorithm for Robust BMI Optimization

Abstract

Robust bilinear matrix inequality (BMI) optimization, which is to minimize an objective function subject to a parameter dependent BMI constraint, is considered. A recursive algorithm employing a branch-and-bound technique and randomization of a parameter is provided for solving the problem. When the algorithm finds a solution, this solution satisfies the parameter dependent constraint with a prescribed accuracy in a probabilistic sense. Furthermore, the objective function value at that solution ensures that the feasible set whose objective function value is less than this value is too small to be found.