A filter method for solving nonlinear complementarity problems

Filter methods are extensively studied to handle nonlinear programming problems recently. Because of good numerical results, filter techniques are attached importance to. In this paper, filter approaches are employed to tackle nonlinear complementarity problems (NCPs). Firstly, NCP conditions are transformed into a nonlinear programming problem. Then, to obtain a trial step, the corresponding nonlinear programming problems are solved by some existing strategies. Moreover, filter criterion is utilized to evaluate a trial iterate. The purpose in this paper is to employ filter approaches to attack NCPs. In essence, multi-objective view is utilized to attack NCPs because the idea of filter methods stems from multi-objective problems. Furthermore, a new filter method, based on the special two objects which differs from others, is brought forward. Moreover, Maratos effects are overcome in our new filter approach by weakening acceptable conditions.