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运筹学学报 ›› 2012, Vol. 16 ›› Issue (2): 1-8.

• 运筹学 •    下一篇

次b凸函数和次b凸规划

晁绵涛1,2, 简金宝3, 梁东颖4   

  1. 1. 北京工业大学应用数理学院，北京，1000124；
    2. 广西教育学院数学与计算机科学系，南宁，530023；
    3. 广西大学数学与信息科学学院，南宁，530004；
    4. 广西交通职业技术学院，南宁，530023
  • 收稿日期:2011-05-30 修回日期:2011-08-21 出版日期:2012-06-15 发布日期:2012-06-15
  • 通讯作者: 梁东颖 E-mail:liangdy_go@126.com
  • 基金资助:

    国家自然科学基金(11171250), 广西自然科学基金(2011GXNSFD018022)

Convex function| sub-b-convex set|  sub-b-convex function| pseudo-sub-b-convex function| optimality conditions

CHAO Miantao1,2, JIAN Jinbao3 , LIANG  Dongying4   

  1. 1.  College of Applied Sciences, Beijing University of Technology, Beijing 100124, China; 2. Department of Mathematics and Computer Science, Guangxi College of Education, Nanning 530023, China; 3. College of Mathematics and Information Science, Guangxi University, Nanning 530004,  China; 4. Guangxi Vocational and Technical College of Communications, Nanning 530023,  China
  • Received:2011-05-30 Revised:2011-08-21 Online:2012-06-15 Published:2012-06-15
  • Supported by:

    National Science Foundation of China

PDF

1404

被引次数

6

摘要：  研究一种称为次b 凸函数的广义凸函数, 并介绍了次b 凸集的概念. 分别在一般情形及可微情形下讨论了次b 凸函数的相关性质, 得到了次b 凸函数成为拟凸函数及伪凸函数的充分条件. 最后, 在次b 凸函数的条件下给出了无约束及带不等式约束规划的最优性条件.

关键词:  凸函数, 次b 凸集合,  , 次b 凸函数,  , 伪次b凸函数, 最优性条件

Abstract: The paper studied a new generalized convex function which called sub-b-convex function, and introduced a new concept of sub-b-convex set. The basic roperties of sub-b-convex functions were discussed in general case and differentiable case, respectively. And, obtained the sufficient conditions that the sub-b-convex function become quasi-convex function or pseudo-convex function. Furthermore, the sufficient conditions of optimality for unconstrained and inequality constrained programming were obtained under the sub-b-convexity.

Key words: convex function, sub-b-convex set, sub-b-convex function, pseudo-sub-b-convex function, optimality conditions