English

运筹学学报 ›› 2012, Vol. 16 ›› Issue (3): 75-83.

• 运筹学 • 上一篇    下一篇

E凸规划问题解集的刻画

姜艮1, 刘学文1, 王岗1, 陈林1   

  1. 1. 重庆师范大学数学系
  • 收稿日期:2010-12-17 修回日期:2012-02-28 出版日期:2012-09-15 发布日期:2012-09-18
  • 通讯作者: 刘学文
  • 基金资助:

    国家自然科学基金(No. 11001289), 重庆市教委科学技术研究基金资助项目(No. KJ100608)

Characterization of solution sets of E-convex programming problems

JIANG Gen1, LIU Xuewen1, WANG Gang1, CHEN Lin1   

  1. 1. Department of Mathematics, Chongqing Normal University
  • Received:2010-12-17 Revised:2012-02-28 Online:2012-09-15 Published:2012-09-18
  • Contact: LIU Xuewen

PDF

1296

被引次数

6

摘要： 考虑一类重要的广义凸规划问题E凸规划. 在E凸集中定义了关于E凸函数的E-Gateaux微分概念, 证明了E凸函数 的E-Gateaux微分的几个特征性质,并利用这些特征性质,提出了E凸规划问题解集的等价刻画. 在赋范向量空间中,对于一个目标函数在最优解处E-Gateaux可微的E凸规划问题而言，它的解集是由位于超平面内的可行解组成的，这些可行解的法向量就是目标函数在给定最优解处的E-Gateaux微分.

关键词: E-Gateaux微分, 解集刻画, E凸函数, E凸规划, 次微分

Abstract: In this paper, an important class of generalized convex programming problems, E-convex program, was considered. We defined the E-Gateaux differential of E-convex function on the E-convex set,  and got some characteristic theorems  of the E-Gateaux differential of E-convex function, proposed the equivalent characterizations of the solution sets of E-convex programming problems by using the characteristic theorems. For an E-convex program in a normed vector space with the objective function admitting the E-Gateaux differential at an optimal solution, we showed that the solution set consists of the feasible points lying in the hyperplane whose normal vector equals the E-Gateaux differential.

Key words: E-gateaux differential, characterization of solution sets, E-convex function, E-convex program, sub-differential

中图分类号: