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仿射变换内点信赖域方法求解变分不等式问题
  • ISSN号：0255-7797
  • 期刊名称：《数学杂志》
  • 时间：0
  • 分类：O224[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]上海立信会计学院数学与信息学院,上海201620, [2]上海师范大学商学院,上海200234
  • 相关基金：Supported by National Natural Science Foundation of China （10871130）.
作者： 王云娟[1], 朱德通[2]
关键词： 变分不等式问题, 仿射变换, 内点, 信赖域, variational inequality problem, affine scaling, interior point, trust region
中文摘要：

本文研究了求解非线性约束变分不等式问题（VIP）的一个新的算法．利用KKT条件的非光滑方程形式，得到了与VIP等价的简单约束优化问题．提出了求解VIP的一类结合回代线搜索技巧的仿射变换内点信赖域算法．在较弱的条件下证明了算法具有整体收敛性，进一步在某些正则条件下，证明了算法具有超线性收敛速度．

英文摘要：

In this article, we study a new algorithm for solving variational inequality problems （VIP） with nonlinear constraints. By using a nonsmooth equation reformulation of the KKT conditions, we analyze an equivalent simply constrained optimization problem of VIP and propose an affine scaling interior trust region method in association with backtracking line search technique for solving VIP. Theoretical analysis are given which prove that the proposed algorithm is globally convergent under mild conditions and further has a local superlinear convergence rate under a certain regularity condition.

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期刊信息
  • 《数学杂志》
  • 北大核心期刊（2011版）
  • 主管单位:中华人民共和国教育部
  • 主办单位:武汉大学 湖北省数学学会 武汉数学学会
  • 主编：陈化
  • 地址：湖北武汉大学
  • 邮编：430072
  • 邮箱：jmath@whu.edu.cn
  • 电话：027-68754687
  • 国际标准刊号：ISSN：0255-7797
  • 国内统一刊号：ISSN：42-1163/O1
  • 邮发代号:38-71
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3910