求解伪单调广义变分不等式的次梯度外梯度算法  

A subgradient extradient algorithm for solving pseudomonotone generalized variational inequalities

作　　者：邹雨航 叶明露[1] ZOU Yuhang;YE Minglu(College of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2023年第4期24-28,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金面上项目(11871059);国家自然科学基金青年项目(11801455)。

摘　　要：2012年Censor等在欧氏空间里提出了一种求解伪单调变分不等式的算法.该算法在映射为Lipschitz连续且伪单调的条件下得到了全局收敛性.基于该算法,将其推广到广义变分不等式,并在集值映射F连续且伪单调的条件下,证明了算法的全局收敛性.数值实验表明了新算法的可行性.In 2012,Censor etc proposed an algorithm for solving pseudo-monotone variational inequalities in Euclidean space.The algorithm achieves global convergence under the condition that the mapping is Lipschitz continuous and pseudo-monotone,based on which the algorithm is extended to generalized variational inequalities,and the global convergence of the algorithm is proved under the condition that the set-valued map is continuous and pseudo-monotone.Numerical experiments are conducted to confirm the feasibility of new algorithm.

关 键 词：广义变分不等式 次梯度外梯度算法 线搜索 伪单调 

分 类 号：O224[理学—运筹学与控制论]