中国民航大学学报

• 基础科学 • 上一篇    

Lipschitz连续强单调逆变分不等式的迭代算法

何松年,刘宏智   

  1. (中国民航大学理学院,天津300300)
  • 收稿日期:2015-05-14 修回日期:2015-06-15 出版日期:2016-04-23 发布日期:2016-06-03
  • 作者简介:何松年(1963—),男,山西太原人,教授,博士,研究方向为非线性分析理论、算法及其应用.
  • 基金资助:

    天津市重点实验室开放课题(1040030603);中国民航大学研究生科技创新基金(Y15-25)

Iterative algorithm for Lipschitz continuous and strongly monotone inverse variational inequalities

HE Songnian, LIU Hongzhi   

  1. (College of Science, CAUC, Tianjin 300300, China)
  • Received:2015-05-14 Revised:2015-06-15 Online:2016-04-23 Published:2016-06-03

摘要:

假设H是一个实的Hilbert 空间,C 是H 的一个非空闭凸子集,f:H→H 是一Lipschitz连续强单调算子。考虑逆变分不等式(简记为IVI(C,f)):即寻求ξ∈H 满足f(ξ)∈C,<ξ,v - f(ξ)>≥0,∀v∈C。证明了IVI(C,f)解的一个存在唯一性定理,给出了解的两个迭代算法袁改进了以往的相关结果。

关键词: 逆变分不等式, 强单调, 不动点, 迭代算法

Abstract:

Let C be a nonempty closed convex subset of a real Hilbert space H, f:H→H be a Lipschitz continuous and strongly monotone mapping. Then, inverse variational inequality is considered (in short, IVI (C, f));find ξ∈H such that f(ξ)∈C,<ξ,v - f(ξ)>≥0,∀v∈C.A new existence and uniqueness theorem for inverse variational inequalities is proved and two iterative algorithms are introduced to improve the previous relevant results.

Key words: inverse variational inequality, strongly monotone, fixed point, iterative algorithm

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