关键词: 绝对值方程;光滑逼近函数;牛顿迭代法;全局收敛性

Abstract:

The absolute value equation(AVE) Ax-|x|=b,A∈R^n×n,b∈Rⁿ is a special class of nonlinear equations and it is NP-Hard.Based on its semi-smoothness,a smoothing Newton method with advanced smoothing function is proposed.Theories indicate this algorithm has a global and quadratic convergence for the singular values of A greater than 1.Numerical results also show that the smoothing Newton method is an easily feasible algorithm.Fianlly,some improved means are given.

Key words: absolute value equation;smoothing advanced function;Newton method;global convergence