A GLOBALLY CONVERGENT METHOD FOR COMPUTING THE FIXED POINT OF SELF-MAPPING ON GENERAL NONCONVEX SET

In this paper, to compute the fixed point of self-mapping on general nonconvex sets with both inequality and equality constraints, the equality constraints are turned into some inequality constraints and a feasible set swelling homotopy is constructed. Under some mild conditions, the existence and global convergence of the smooth homotopy pathways is also proved. Compared with the previous results, the initial point is not needed to be a feasible interior point of the original feasible set, and can be chosen freely in a bounded ball region of the shifted feasible set. Some numerical examples are also given to show the feasibility and effectiveness of the homotopy method.