强G-半预不变凸性与非线性规划问题

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

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.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-xi^1,2

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/Abstract

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

彭再云, 孔祥茜. 强G-半预不变凸性与非线性规划问题[J]. 广西师范大学学报（自然科学版）, 2013, 31(1): 48-53.

PENG Zai-yun, KONG Xiang-xi. Strongly Semi-G-preinvexity and Nonlinear Programming[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(1): 48-53.

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