2024年12月26日 星期四

广西师范大学学报(自然科学版) ›› 2013, Vol. 31 ›› Issue (1): 48-53.

• • 上一篇    下一篇

强G-半预不变凸性与非线性规划问题

彭再云1, 孔祥茜1,2   

  1. 1.重庆交通大学理学院,重庆400074;
    2.吉林大学管理学院,吉林长春130022
  • 收稿日期:2012-09-13 出版日期:2013-03-20 发布日期:2018-11-26
  • 通讯作者: 彭再云(1980—),男,重庆人,重庆交通大学副教授,内蒙古大学博士研究生。E-mail:pengzaiyun@126.com
  • 基金资助:
    国家自然科学基金资助项目(11271389);国家青年基金资助项目(11201509);重庆市自然科学基金资助项目(CSTC2011AC6104,2012jjA00016);重庆市教委基金资助项目(KJ120401)

Strongly Semi-G-preinvexity and Nonlinear Programming

PENG Zai-yun1, KONG Xiang-xi1,2   

  1. 1.College of Science,Chongqing Jiaotong University,Chongqing400074,China;
    2.School of Management,Jilin University,Changchun Jilin 130022,China
  • Received:2012-09-13 Online:2013-03-20 Published:2018-11-26

摘要: 本文提出一类新的广义凸函数——强G-半预不变凸函数,它是一类重要的广义凸函数,是半预不变凸函数与强G-预不变凸函数的真推广。首先,用例子验证强G-半预不变凸函数的存在性,并举例说明它区别于强预不变凸函数;然后探讨强G-半预不变凸函数的性质与几何刻画;最后,给出强G-半预不变凸函数在非线性规划中的几个应用,得到了一些最优性结果,并举例验证结论的正确性。

关键词: 半连通集, 非线性规划, 强预不变凸函数, 强G-半预不变凸函数

Abstract: A class of new generalized convex function,strongly semi-G-preinvex function,is given in this paper.It is an important class ofgeneralized convex function.It is a true generalization of semi-preinvex functions and strongly G-preinvex functions.First,an example is given to show that there exists strongly semi-G-preinvex function.At the same time,an example is given to show that strongly semi-G-preinvex function is different from strongly preinvex functions.Then,some properties of strongly semi-G-preinvex functions are discussed.Finally,some optimal results are obtained in nonlinear programming problems,and an example is also given for illustration of the corresponding results.

Key words: semi-connected sets, nonlinear programming, stronglypreinvex functions, strongly semi-G-preinvex functions

中图分类号: 

  • O221.1
[1] WEIR T,MOND B.Pre-invex functions in multiple objective optimization[J].J Math Anal Appl,1988,136(1):29-38.
[2] ANTCZAK T.G-pre-invex functions in mathmatical programming[J].J Comput Appl Math,2008,217(1):212-226.
[3] 颜丽佳,刘芙萍.强预不变凸函数[J].重庆师范大学学报:自然科学版,2005,22(1):11-15.
[4] YANG X Q,CHEN Guang-ya.A class of nonconvex functions and pre-variational inequalities[J].J Math Anal Appl,1992,169(2):359-373.
[5] 彭再云,房效亮,赵勇.强G-预不变凸函数[J].重庆师范大学学报:自然科学版,2011,28(6):1-4,12.
[6] 彭再云,周选林,赵勇.强G-预不变凸函数的性质及应用[J].重庆师范大学学报:自然科学版,2012,29(4):12-17.
[7] YANG Xin-min,LI Duan.On properties of preinvex functions[J].J Math Anal Appl,2001,256(1):229-241.
[8] ANTCZAK T.New optimality conditions and duality results of G type in differentiable mathematical programming[J].Nonlinear Analysis,2007,66(7):1617-1632.
[9] MISHRA S K,GIORGI G.Invexity and optimization:nonconvex optimization and its applications[M].Berlin:Spring-er,2008.
[10] PENG Zai-yun.Semistrictly G-preinvexity and its applications[J].Journal of Inequalities and Applications,2012(9):198.
No related articles found!
Viewed
Full text
143
HTML PDF
Just accepted Online first Issue Just accepted Online first Issue
0 0 0 0 0 143

  From local
  Times 143
  Rate 100%

Abstract
84
Just accepted Online first Issue
0 0 84
  From Others
  Times 84
  Rate 100%

Cited

Web of Science  Crossref   ScienceDirect  Search for Citations in Google Scholar >>
 
This page requires you have already subscribed to WoS.
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报(自然科学版)编辑部
地址:广西桂林市三里店育才路15号 邮编:541004
电话:0773-5857325 E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发