The ODE-type Filter Methods For Nonlinear Complementarity Problems

The nonlinear complementarity problems contains a complementary relationship between the two sets of decision variables.There are many types of complementarity problems.In this paper,discuss the general nonlinear complementarity problems are discussed,which are risen in many fields,such as economic equilibrium with problems,circuit connection problem in Engineering,fluid mechanics problems,optimal control problems and so on.Thus,it is meaningful to find the solution of the nonlinear complementarity problems.The nonlinear complementarity problems is converted into constrained optimization in this paper.For solving constrained optimization problems,Fletcher and Leyffer proposed a class of filter methods which have promising numerical results.A quadratic subproblem is needed to obtain the search direction in their method,which result in the large computational amount.On the other hand,only the objective function is included in a traditional filter set not other information.To modify the above shortcomings,based on the idea of ordinary differential equation method,we propose modified filter methods for nonlinear complementarity problems.Compared with the traditional filter methods,our methods are more flexible and easier to implement.Under some reasonable conditions,the global convergence properties of algorithms are presented.