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

Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.