箱约束变分不等式的一种新NCP-函数及其广义牛顿法

１．引 言设，变分不等式，记为ＶＩ（Ｘ，Ｆ），是指：求ｘ＝Ｘ使记为箱式约束时，称 ＶＩ（Ｘ，Ｆ）为箱约束变分不等式，记为 ＶＩ（［ａ，ｂ］，Ｆ）．若ａｉ＝０，ｂｉ＝＋∞，　　　　　　　　　　　　　　　　　　　　　　　　　为非线性互补问题ＮＣＰ（Ｆ）：求ｘ∈Ｒ

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

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.