箱约束变分不等式的一种新NCP-函数及其广义牛顿法  

A NEW NCP-FUNCTION FOR BOX CONSTRAINED VARIATIONAL INEQUALITYS AND A RELATED NEWDON-TYPE METHOD

作　　者：陈国庆[1] 曹兵[1] 

机构地区：[1]内蒙古大学理工学院数学系,呼和浩特010021

出　　处：《计算数学》2002年第1期91-104,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金(19701016);高等学校骨干教师资助计划资助

摘　　要：A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equa- tions whose merit function is differentiable every where. For the P0-function F, any stationary point of the merit function solves the VI([a, b], F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equa- tions whose merit function is differentiable every where. For the P0-function F, any stationary point of the merit function solves the VI([a, b], F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.

关 键 词：箱约束变分不等式 NCP-函数 半光滑方程组 广义牛顿法 

分 类 号：O242.2[理学—计算数学]