Abstract

We consider a nonlinear complementarity problem defined by a continuous but not necessarily locally Lipschitzian map. In particular, we examine the connection between solutions of the problem and stationary points of the associated Fischer-Burmeister merit function. This is done by deriving a new necessary optimality condition and a chain rule formula for composite functions involving continuous maps. These results are given in terms of approximate Jacobians which provide the foundation for analyzing continuous nonsmooth maps. We also prove a result on the global convergence of a derivative-free descent algorithm for solving the complementarity problem. To this end, a concept of directional monotonicity for continuous maps is introduced.