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.

In this paper, to compute the fixed point of self-mapping on general non-convex 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.

In this paper, a modified iterative algorithm for finding a common element of the solutions of a equilibrium problem, the set of fixed points of nonexpansive mappings and the set of solutions of variational inequality problem is constructed in Hilbert spaces, and the strong convergence of the generated iterative sequence to the common element is proved under some mild conditions. The main result proposed in this paper extends and improves some recent results in the literature. c 2017 all rights reserved.