Inexact Trust-Region Methods for Nonlinear Complementarity Problems

Abstract

In order to solve the nonlinear complementarity problem, we first reformulate it as a nonsmooth system of equations by using a recently introduced NCP-function. We then apply a trust-region-type method to this system of equations. Our trust-region method allows an inexact solution of the trustregion-subproblem. We show that the algorithm is well-defined for a general nonlinear complementarity problem and that it has some nice global and local convergence properties. Numerical results indicate that the new method is quite promising.