A modified homotopy method for solving nonconvex fixed points problems

摘要

In the paper, to compute the fixed point of a self-mapping in a class of nonconvexunbounded sets with both inequality and equality constraints, a modified homotopy is constructedand the existence and convergence of the smooth homotopy pathways is proved under mild conditions.Compared with the previous results, the modified combined homotopy method needs only weakerconditions. Some numerical examples are given to show the feasibility and effectiveness of theproposed method.