Convergence analysis of a block improvement method for polynomial optimization over unit spheres

Abstract

In this paper, we study the convergence property of a block improvement method (BIM) for the bi-quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second-order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising.