An Interior-point Algorithm for Mixed Complementarity Problems

1. Abstract Complementarity problems arise in mathematical models of several applications in Engineering, Economy and different branches of Physics. We mention contact problems and dynamic of multiple body systems in Solid Mechanics. In this paper we present a new feasible directions interior-point algorithm for mixed nonlinear complementarity problems that we have called FDA-MNCP. This algorithm is an extension of the FDA-NCP, an algorithm for complementarity problems recently proposed by the authors. The FDA-MNCP begins at any point strictly satisfying the inequality conditions and generates a sequence of interior points that converges to a solution of the problem. The sequence of iterates is generated in such a way that a suitable potential function is monotonically reduced. At each iterate, the algorithm finds a feasible direction, with respect to the region defined by the inequality conditions, which is also descent for the potential function. Then, an inexact line search along this direction is performed in order to define the next iterate. Results about global and asymptotic convergence for the FDA-MNCP algorithm are stated. Numerical results obtained with the proposed algorithm for several well known benchmark problems are presented. These results agree with the asymptotic analysis and show that the FDA-MNCP algorithm is efficient and robust.