A power penalty approach to a Nonlinear Complementarity Problem

We propose a novel power penalty approach to a Nonlinear Complementarity Problem (NCP) in which the NCP is approximated by a nonlinear equation containing a power penalty term. We show that the solution to the penalty equation converges to that of the NCP at an exponential rate when the function involved is continuous and ξ-monotone. A higher convergence rate is also obtained when the function becomes Lipschitz continuous. Numerical results are presented to confirm the theoretical findings.