变分不等式的一种自适应算法

中国民航大学学报

变分不等式的一种自适应算法

何松年，罗标

（中国民航大学理学院，天津300300）

收稿日期:2013-04-11 修回日期:2013-07-15 出版日期:2014-06-24 发布日期:2014-10-31
作者简介:何松年（1963—），男，山西太原人，教授，博士，研究方向为非线性问题计算方法.
基金资助:
中央高校基本科研业务费专项（3122013k004）

Self-adaptive algorithm for variational inequalities

HE Song-nian,LUO Biao

(College of Science,CAUC,Tianjin 300300,China)

Received:2013-04-11 Revised:2013-07-15 Online:2014-06-24 Published:2014-10-31

摘要/Abstract

摘要：

提出求解定义在实Hilbert空间闭凸集上Lipschitz强单调变分不等式唯一解的一种自适应算法，即以一种自适应的方式在每一步迭代计算时确定计算格式中的迭代步长，无需计算或估计其中非线性算子的Lipschitz常数和强单调系数，从而使得该算法更容易实现。证明了算法的强收敛性。

关键词: 自适应算法, 变分不等式, 强收敛, Hilbert空间

Abstract:

A self-adaptive algorithm is proposed to solve the Lipschitz and strongly monotone variational inequality defined on a closed convex subset in a real Hilbert space. Since this method selects stepsizes via a selfadaptive way,i.e.,has no need to estimate the Lipschitz constant and strong monotone coefficient,its implementation is rather easy. Strong convergence of the algorithm is proved.

Key words: self-adaptive algorithm, variational inequality, strong convergence, Hilbert space

中图分类号:

O178

何松年，罗标. 变分不等式的一种自适应算法[J]. 中国民航大学学报.

HE Song-nian,LUO Biao. Self-adaptive algorithm for variational inequalities[J]. .

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