BMI optimization based on unimodal normal distribution crossover GA with relaxed LMI convex estimation

This paper deals with the global optimization of the BMIEP (bilinear matrix inequalities eigenvalue problem) based on the UNDX (unimodal normal distribution crossover) GA. First, analyzing the structure of the BMIEP, the existence of the typical difficult structures is confirmed. Then, based on the results of the problem structures analysis and the consideration of the BMIEP characteristic properties, an efficient UNDX GA algorithm with LMI convex estimation is proposed. The effectiveness of the proposed algorithm is evaluated by several numerical examples.