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 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.

非线性互补问题的一类光滑逼近函数

通过NCP-函数,非线性互补问题可以转化为求解一个非光滑方程组,利用光滑逼近函数可以用一个光滑方程组逼近该非光滑方程组。本文提出了一类新的光滑逼近函数,它是Chen和Harker提出的变尺度内点光滑函数的推广,并证明了该类光滑函数和变尺度内点光滑函数具有相同的重要性质的。因此,该类光滑函数适用于线性互补问题的非内点路径跟踪算法。

基于带参数价值函数求解线性互补问题的信赖域算法

基于带参数价值函数,给出了求解线性互补问题LCP(q,M)的信赖域算法.在每步迭代时,仅需求解简单的线性方程组.在M为P-矩阵时,算法全局收敛.无需假设极限点x*是否退化,在一定的条件下,算法局部超线性收敛.

变分不等式的一种改进的拟牛顿法

构造了一个具有二次光滑性的NCP函数,通过它将变分不等式问题转化为无约束优化问题,用一种改进的拟牛顿算法对其进行求解,有效地弥补了以往的拟牛顿算法要求目标函数具有凸性或一致凸性的缺陷,在更弱的条件下讨论了算法的收敛性质。

非线性互补问题转化为无约束优化问题的方法

本文介绍一种带参数的NCP-函数,从而将非线性互补问题(NCP(F))先转化为非光滑方程组的形式,再引进相应价值函数等价地转化为无约束最优化问题的方法,并且还讨论了此NCP-函数,非光滑方程组和相应价值函数的性质。