A New Method for Solving Non-Linear Complementarity Problems

The non-linear complementarity problem NLCP is to find a vector z in IR satisfying 0 6 z ⊥ f(z) > 0, where f is a given function. This problem can be solved by several methods but the most of these methods require a lot of arithmetic operations, and therefore, it is too difficult, time consuming, or expensive to find an approximate solution of the exact solution. In this paper we give a new method for solving this problem which converges very rapidly relative to most of the existing methods and does not require a lot of arithmetic operations to converge. For this we show that solving the NLCP is equivalent to finding zero of the function F . After we build a sequence of smooth functions F (k) ∈ C∞ which is uniformly convergent to the function F and we show that, an approximation of the solution of the NLCP is obtained by solving F (x) = 0 for a parameter k large enough. We close our paper with some numerical examples to demonstrate the efficiency of our method. The numerical results obtained in this paper are very favorable and showed that our method works well for the problems tested.