Convergent algorithm based on progressive regularization for solving pseudomonotone variational inequalities

作     者：El Farouq, N 

作者机构：Univ Clermont Ferrand Toulouse France CNRS LAAS F-31077 Toulouse France 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：2004年第120卷第3期

页      面：455-485页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：variational inequalities generalized monotonicity pseudomonotonicity regularization convergence of algorithms decomposition 

摘      要：In this paper, we extend the Moreau-Yosida regularization of monotone variational inequalities to the case of weakly monotone and pseudomonotone operators. With these properties, the regularized operator satisfies the pseudo-Dunn property with respect to any solution of the variational inequality problem. As a consequence, the regularized version of the auxiliary problem algorithm converges. In this case, when the operator involved in the variational inequality problem is Lipschitz continuous (a property stronger than weak monotonicity) and pseudomonotone, we prove the convergence of the progressive regularization algorithm introduced in Refs. 1, 2.