A homotopy algorithm for computing the fixed point of self-mapping with inequality and equality constraints

In this paper, to compute the fixed point of selfmapping on general nonconvex sets, a modified constraint shifting homotopy algorithm for perturbing simultaneously both equality constraints and inequality constraints is proposed and the global convergence of the smooth homotopy pathways is proven under some mild conditions. The advantage of the newly constructed homotopy is that the initial point needs to be only in the shifted feasible set, not necessarily, an interior point in the original feasible set, and hence it is more convenient to be implemented than the existing results. Some numerical examples are also given to show its feasibility and effectiveness.