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运筹学学报 ›› 2013, Vol. 17 ›› Issue (3): 124-128.

• 运筹学 • 上一篇    

关于局部凸空间中向量Ekeland变分原理的等价性

万轩1, 赵克全2,*   

  1. 1. 重庆电讯职业学院基础部, 重庆 402247 2. 重庆师范大学数学学院, 重庆 401331
  • 出版日期:2013-09-15 发布日期:2013-09-15
  • 通讯作者: 赵克全 E-mail:kequanz@163.com
  • 基金资助:

    国家自然科学基金(Nos. 11271391, 11301574), 重庆自然科学基金(No. cstc2012jjA00002)

Equivalence on vectorial Ekeland's variational principle in locally convex space

WAN Xuan1, ZHAO Kequan2,*   

  1. 1.  Department of Foundation, Chongqing Telecommunication Polytechnic College, Chongqing 402247, China 2.  College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China
  • Online:2013-09-15 Published:2013-09-15

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被引次数

2

摘要： 基于各种Ekeland变分原理的等价形式, 主要研究局部凸空间中给定有界凸子集乘以距离函数为扰动的单调半连续映射的向量Ekeand变分原理的等价性问题. 首先利用局部凸空间中的向量Ekeland变分原理证明了向量Caristi-Kirk不动点定理，向量 Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理. 进一步研究了向量Ekeland变分原理与向量Caristi-Kirk不动点定理，向量Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理的等价性.

关键词: 向量Ekeland变分原理, 向量Caristi-Kirk不动点定理, 向量Takahashi非凸极小化定理, 向量Oettli-Th\'{e}ra定理, 等价性

Abstract: In this paper, based on equivalent formulations of various types of Ekeland's variational principle, we consider the equivalence on vectorial Ekeland's variational principle for monotonically semicontinuous mappings with perturbations given by a convex bounded subset of directions multiplied by the distance function in locally convex spaces. Firstly, by using a vectorial Ekeland's variational principle in locally convex spaces, we present a simple proof of vectorial Caristi-Kirk's fixed-point theorem, vectorial Takahashi's nonconvex minimization theorem and vectorial Oettli-Th\'{e}ra's theorem. Furthermore, we study the equivalence among the vectorial Ekeland's variational principl, the vectorial Caristi-Kirk's fixed-point theorem, the vectorial Takahashi's nonconvex minimization theorem and the vectorial Oettli-Th\'{e}ra's theorem.

Key words: vectorial Ekeland's variational principle, vectorial Caristi-Kirk's fixed-point theorem, vectorial Takahashi's nonconvex minimization theorem, vectorial Oettli-Th\'{e}ra's theorem, equivalence

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