SOLVING STRONGLY MONOTONE VARIATIONAL AND QUASI-VARIATIONAL INEQUALITIES

被引：49
|
作者：
Nesterov, Yurii [1 ]
Scrimali, Laura [2 ]
机构：
[1] Catholic Univ Louvain, CORE, B-1348 Louvain, Belgium
[2] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 31卷 / 04期
关键词：
Variational inequality; quasi-variational inequality; monotone operators; complexity analysis; efficiency estimate; optimal methods; OPTIMIZATION PROBLEMS;
D O I：
10.3934/dcds.2011.31.1383
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequalities. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutions. Moreover, we get a new numerical scheme, whose rate of convergence is much higher than that of the straightforward gradient method.
引用
收藏
页码：1383 / 1396
页数：14
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