求解广义张量绝对值方程的光滑化牛顿算法  

A Smoothing Newton Method for Tensor Generalized Absolute Value Equations

作　　者：郭旭 谷伟哲 GUO Xu;GU Weizhe(School of Mathematics,Tianjin University,Tianjin,300350,P.R.China)

机构地区：[1]天津大学数学学院,天津300350

出　　处：《数学进展》2020年第6期761-768,共8页Advances in Mathematics（China）

基　　金：Supported by NSFC (No.11871051)。

摘　　要：本文提出了一种求解广义张量绝对值方程的光滑化牛顿算法.广义张量绝对值方程是对矩阵广义绝对值方程的推广,目前得到了广泛的关注.我们证明了在一种弱且容易验证的条件下,光滑牛顿算法是有全局收敛性的,同时我们给出了数值实验来说明算法的有效性.In this paper,we propose a smoothing Newton method to solve the tensor generalized absolute value equations(TGAVEs).TGAVEs are a generalization of matrix generalized absolute value equations(GAVEs) and nowadays have attracted a lot of attention.Under a weak and easily checkable condition,the smoothing Newton method is proved to be globally convergent.We also give some numerical results,which show that the algorithm is efficient.

关 键 词：张量绝对值方程 光滑牛顿算法 强P0张量 

分 类 号：O224[理学—运筹学与控制论]