Multi-Valued Implicit Complementarity Problems: Perturbation Algorithm

In this paper, we present a method to solve multivalued implicit complementarity problems using a perturbation approach. First, we establish the existence of solutions to a perturbed multi-valued implicit complementarity problem with parameters. Then we show the convergence of selections of the solutions of the perturbed problem to a solution of the original problem and examine the convergence rate. Finally, we propose a numerical algorithm of the prediction- correction type to solve the multi-valued perturbed problem at each step. Convergence of this procedure is demonstrated as well.