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

✍ Scribed by Changfeng Ma; Xiaohong Chen

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
180 KB
Volume
216
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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