A modified infeasible homotopy algorithm for computing fixed point in general non-convex set

In this paper, to find a fixed point of self-mapping in the general non-convex set with both equality constraints and inequality constraints, a modified infeasible homotopy for perturbing only inequality constraints is constructed and the global convergence of the smooth homotopy pathways is proved under some much weaker conditions. The advantage of the modified homotopy is that the initial point needs to be only in the shifted set with only inequality constraints, not necessarily, a feasible point in the original set, and hence it is more convenient to be implemented than the existing methods. The feasibility and effectiveness of the modified homotopy method is shown by some numerical tests.