An Inexact Smoothing Newton Method For Solving P₀-NCP Problems

The complementarity problem is an interdisciplinary research area of Op-erations Research and Computational Mathematics. Because its close contactwith the branches of mathematics optimization, variational inequalities, balanceproblems, game theory, fixed point theory and extensive applications, the comple-mentarity problem became more and more important. In this paper, an inexactsmoothing Newton method for solving the nonlinear complementarity problemwas developed. This method was based on a smooth symmetric perturbationFischer Burmeister function and aimed to overcome the complexity of the linearsubsystems with reducing computation for obtaining the approximate solution ofNCP. The new algorithm performed global and superlinear convergence withoutstrict complementarity under mild conditions. Furthermore, numerical experi-ments demonstrated the feasibility and high efciency of the new algorithm forsolving large-scale problems.