A New Interior Point Algorithm for Nonlinear Complementarity Problems

The complementarity problem consists in finding x ∈ IR n such that x ≥ 0,F (x) ≥ 0 and x t F (x) =0, where F:IR n → IR n. Complementarity problems are involved in several applications in engineering, economy and different branches of physics. We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible interior point algorithm for nonlinear complementarity problems. This algorithm begins at a point that verifies the inequality conditions of the problem and generates a sequence of points that also verify them. The numerical results obtained with several numerical test problems, and also with contact problems, are presented. Here the problems were solved very efficiently when compared with other methods. The present approach is also very strong; all the results were obtained with the same set of parameters. 2