BMI Global Optimization using Parallel Branch and Bound Method with a Novel Branching Method

This paper deals with the global optimization of the BMIEP (bilinear matrix inequalities eigenvalue problem) based on a parallel branch and bound method. First, a novel branching rule considering BMI structure is proposed for both serial and parallel algorithms. Comparing the proposed branching rule with conventional ones, we confirm the effectiveness of the new branching method. Then, based on a master-worker method, a parallelized branch and bound algorithm is designed and implemented on a Beowulf cluster system. The computational granularity is an important factor for the efficiency of parallel algorithms. The developed parallel algorithm makes the computational granularity variable. The effectiveness of the maximal granularity parameter optimization is numerically studied. Finally, a low-order H_infin controller design problem is solved to demonstrate the viability of both the developed algorithm and the implemented software.