求解非线性方程组的一个光滑化一步牛顿算法

A One-step Smoothing Newton Method for Solving Nonlinear Equation

针对非线性非光滑函数方程组提出了一种新的光滑化一步牛顿算法,这个算法的每步迭代只需要解1个线性方程组,执行1次线搜索.证明了该算法是全局收敛的,并且在一定条件下,证明了它的局部超线性收敛性和二次收敛性.

This paper presents a one-step smoothing Newton method for solving nonlinear nonsmooth system of equations. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. The proposed algorithm is proved to be convergent globally and superlinearly/quadratic convergence under suitable assumptions.