A penalty method for a mixed nonlinear complementarity problem

We propose a power penalty method for a mixed nonlinear complementarity problem (MNCP) and show that the solution to the penalty equation converges to that of the MNCP exponentially as the penalty parameter approaches infinity, provided that the mapping involved in the MNCP is both continuous and ξξ-monotone. Furthermore, a convergence theorem is established when the monotonicity assumption on the mapping is removed. To demonstrate the usefulness and the convergence rates of this method, we design a non-trivial test MNCP problem arising in shape-preserving bi-harmonic interpolation and apply our method to this test problem. The numerical results confirm our theoretical findings.