基于模量重构的张量互补问题的光滑牛顿算法

A Smoothing Newton Algorithm for Tensor Complementarity Problem Based on the Modulus-Based Reformulation

近年来,张量作为矩阵的推广,得到了广泛的研究.在众多张量相关的问题中,张量互补问题(TCP)是许多学者研究的一个重要领域,人们提出了许多解决TCP的方法.本文在强P-张量张量和光滑逼近函数的基础上,提出一种基于基于模的重构的TCP光滑牛顿算法,证明光滑牛顿方法是全局收敛的.数值算例验证了光滑牛顿算法的有效性.

In the recent past few years,tensor,as the extension of the matrix,is well studied.Among many tensor related problems,the tensor complementarity problem(TCP)is a useful area for many researchers to study,and many methods to solve TCP have been proposed.In this article,under the condition of a strong P-tensor,we propose a smoothing Newton method to solve TCP based on the modulus-based reformulation,and we prove that the smoothing Newton method is globally convergent.Some numerical examples are given to demonstrate the efficiency of the smoothing Newton algorithm.