带新的非线性互补函数的广义非精确牛顿法

Inexact Generalized Newton Method with New NCP Function

提出了新的弱正则伪光滑非线性互补(NCP)函数,该函数具有良好的性质.在这个新的NCP函数基础上,求解一个目标函数和约束函数都是光滑的最优化问题.构造半光滑方程组,用来求解非线性约束最优化问题的KKT点,然后用新提出的广义非精确牛顿法解这个半光滑方程组.该方法是可实现的,且具有全局收敛性.最后还证明了在较弱假设条件下,它具有局部超线性收敛性.

In this paper,we present a new nonlinear complementarity （NCP） function which is piecewise linear-rational, regular pseudo-smooth and has nice properties. Then we apply the NCP function to some nonlinear optimization methods. We reformulate the problem for finding KKT points of the nonlinear constrained optimization problem as a system of semismooth equations by using the new NCP function. Then we consider the local behavior of inexact generalized Newton methods to solve the semismooth equations. The method is implementable and globally convergent. We also prove that the algorithm has superlinear convergence rates under some mild conditions.