Anderson加速外梯度法求解非线性互补问题  

Anderson Acceleration of the Extragradient Method for the Nonlinear Complementarity Problems

作　　者：张汇实 张天四[1] 薛文娟[2] 

机构地区：[1]上海理工大学(理学院),上海200093 [2]上海电力学院(数理学院),上海200090

出　　处：《应用数学》2018年第1期229-236,共8页Mathematica Applicata

基　　金：国家自然科学基金(11601318)

摘　　要：外梯度法是一种可以用来解决非线性互补问题的常规算法,其计算简单,存储小,但是收敛速度比较慢.本文基于Anderson加速的思想对其进行改进,从理论上证明了新算法的收敛性,并在数值实验上表明该算法不仅比原始算法加速明显,也比投影收缩算法性能优越,而且在大规模问题上的加速效果稳定.The extragradient method is a general tool to solve the nonlinear complementarity problems（NCP）, which requires less memory and is easy to be implemented, but has a slow convergence.This paper improves it by using Anderson Acceleration and proves the convergence of the new algorithm in theory. In the numerical experiment, it shows that the improved algorithm has better performance than the original method and the projection and contraction methods as well. Besides, it has a steady effect of acceleration in high-dimensional problems.

关 键 词：Anderson加速 外梯度法 非线性互补问题 

分 类 号：O224[理学—运筹学与控制论]