A new class of smoothing functions and a smoothing Newton method for complementarity problems

In this paper, we introduce a new class of smoothing functions, which include some popular smoothing complementarity functions. We show that the new smoothing functions possess a system of favorite properties. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P ₀ function are discussed. The Jacobian consistency of this class of smoothing functions is analyzed. Based on the new smoothing functions, we investigate a smoothing Newton algorithm for the NCP and discuss its global and local superlinear convergence. Some preliminary numerical results are reported.