Computational Complexity Analysis of Global Optimization for the Matrix Product Eigenvalue Problem

Abstract

In this paper, we demonstrate a computational complexity analysis of the global optimization for the Matrix Product Eigenvalue Problem (MPEP). A global optimization scheme for the MPEP is compared with other nonconvex optimization problems such as Convex Multiplicative Programming (CMP) and branch and bound methods for solving Bilinear Matrix Inequality (BMI) problems. We show that convex subproblems for the MPEP global optimization algorithm are solved more efficiently than those of the BMI branch and bound methods. Numerical experiments illustrate that the MPEP global optimization algorithm achieves less number of iterations and CPU-time than the BMI branch and bound methods even in the total computational complexity.