A constraint shifting homotopy method for computing fixed points on nonconvex sets

In this paper, a constraint shifting homotopy method for solving fixed point problems on nonconvex sets is proposed and the existence and global convergence of the smooth homotopy pathways is proved under some mild conditions. Compared with the previous results, the newly proposed homotopy method requires that the initial point needs to be only in the shifted feasible set not necessarily in the original feasible set, which relaxes the condition that the initial point must be an interior feasible point. Some numerical examples are also given to show the feasibility and effectiveness of our method.