The convergence of a one-step smoothing Newton method for P0-NCP based on a new smoothing NCP-function

Authors:
Changfeng Ma;Xiaohong Chen
Affiliations:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China and School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 54100 ...;School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

The nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the solution of a nonsmooth system of equations. By introducing a new smoothing NCP-function, the problem is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is proposed for solving the nonlinear complementarity problem with P"0-function (P"0-NCP) based on the new smoothing NCP-function. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. Without requiring strict complementarity assumption at the P"0-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions.