An interior-point derivative-free algorithm for nonlinear complementarity problems

In this paper, we propose an interior-point derivative-free algorithm for nonlinear complementarity problems (NCPs). The function F involved in the NCP is assumed to be continuously differentiable and monotone. The new algorithm maintains the non-negativity of iterates. It has some advantages: one is to avoid stationary points with negative components which are not the solutions of NCPs, and the other is to be useful for F defined on non-negative domain. Furthermore, we design a filter according to the algorithm, which does not contain a gradient of F. Under some assumptions, we discuss the global convergence of the new algorithm. Numerical results demonstrate that the new algorithm is effective.