求解单调变分不等式的修正次梯度外梯度算法  

A Modified Subgradient Extragradient Algorithm forSolving Monotone Variational Inequality

作　　者：陈家欣 叶明露[1] CHEN Jiaxin;YE Minglu(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,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：《西华师范大学学报（自然科学版）》2021年第1期23-28,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059,11801455)。

摘　　要：本文提出了求解映射单调且Lipschitz连续变分不等式的修正次梯度外梯度算法。新算法在已有投影算法的基础上给出了新的步长规则,这使得新算法能适用于映射是Lipschitz连续但其系数是未知的变分不等式问题。在适当的假设条件下证明了算法所产生的序列能弱收敛到变分不等式问题的解。因此,该算法改进并拓展了文献中的一些结果。A modified subgradient extragradient algorithm for solving monotone and Lipschitz continuous variational inequality problems is presented in this paper.This algorithm gives a new step rule based on the existing projection algorithm.Therefore,the proposed algorithm is suitable for solving variational inequality problems whose underlying mapping is Lipschitz continuous with unknown Lipschitz modulus.It is proved that the sequence generated by this algorithm is weakly convergent to the solution of variational inequality problems under some mild assumptions.Hence,the new algorithm is an improvement and extension of some results in the literature.

关 键 词：次梯度外梯度算法 单调 LIPSCHITZ连续 HILBERT空间 变分不等式 

分 类 号：O221[理学—运筹学与控制论]