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We consider a class of complementarity problems involving functions which are not Lipschitz continuous. In this paper we reformulate this class of non-Lipschitzian complementarity problems into a Lipschitzian complementarity problem. Then we propose an inexact smoothing Newton method to solve this Lipschitzian complementarity problem. We prove that our proposed method converges quadratically and globally under a mild condition. Numerical results show that this method is promising. This method can solve these kinds of complementarity problems with one million variables in reasonable time on a PC with 1 GB of RAM.

A Superlinearly Convergent Method for a Class of Complementarity Problems with Non-Lipschitzian Functions