一类非线性互补问题的新修正谱梯度投影方法  

A New Modified Spectral Gradient Projection Method for a Class of Nonlinear Complementarity Problems

作　　者：林婷[1] 柯艺芬 张振 马昌凤[1] LIN Ting;KE Yifen;ZHANG Zhen;MA Changfeng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Key Laboratory of Computational Geodynamics,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]中国科学院大学计算地球动力学重点实验室,北京100049

出　　处：《福建师范大学学报（自然科学版）》2022年第5期34-42,共9页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家重点研发计划资助项目(2019YFC0312003);国家自然科学基金资助项目(11901098)。

摘　　要：提出了一类求解非线性互补问题的新修正谱梯度投影方法.首先,将非线性互补问题等价地表述为一个非线性方程组.进而,提出一类新的修正谱梯度投影方法求解所得的非线性方程组.新方法具有如下特点:谱梯度主要由修正的长Barzilli-Borwein步长和修正的短Barzilli-Borwein步长的凸组合决定,并采用了一种新的线搜索技术.数值实验证明所提出的方法能够有效地求解非线性互补问题.A new modified spectral gradient projection method for nonlinear comple-mentarity problems is presented.Firstly,the nonlinear complementarity problem considered in this paper is equivalently expressed as a nonlinear equation,and then a new modified spectral gradient projection method is proposed to solve the derived nonlinear equation.The characteristics of the proposed method are as follows:the spectral gradient is mainly determined by the convex combination of the modified long Barzilli-Borwein step and the modified short Barzilli-Borwein step,and a new line search technique is used.Numerical experiments show that the proposed algorithm can effectively solve the nonlinear complementarity problem.

关 键 词：非线性互补问题 谱梯度投影 全局收敛性 

分 类 号：O241.7[理学—计算数学]