Superlinear/Quadratic One-step Smoothing Newton Method for P_0-NCP  

作　　者：LiPingZHANG JiYeHAN ZhengHaiHUANG 

机构地区：[1]DepartmentofMathematicalSciences,TsinghuaUniversity,Beijing100084,P.R.China [2]InstituteofAppliedMathematics,AcademyofMathematics&:SystemsScience,ChineseAcademyofSciences,Beijing100080,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2005年第1期117-128,共12页数学学报（英文版）

基　　金：This work is partly supported by the National Natural Science Foundation of China(Grant,Nos.10271002,10201001)

摘　　要：We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.

关 键 词：non–linear complementarity problems Smoothing Newton method Superlinear/quadratic convergence 

分 类 号：O242.23[理学—计算数学]