A smoothing Newton method for NCPs with the P0‐property

In this paper, we first investigate a two‐parametric class of smoothing functions which contains the penalized smoothing Fischer–Burmeister function and the penalized smoothing CHKS function as special cases. Then we present a smoothing Newton method for the nonlinear complementarity problem based on the class of smoothing functions. Issues such as line search rule, boundedness of the level set, global and quadratic convergence are studied. In particular, we give a line search rule containing the common used Armijo‐type line search rule as a special case. Also without requiring strict complementarity assumption at the P0‐NCP solution or the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Preliminary numerical results show the efficiency of the algorithm and provide efficient domains of the two parameters for the complementarity problems.