半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究

彭再云; 孙佳徽; 李科科; 张石生

doi:10.21656/1000-0887.370280

半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究

doi: 10.21656/1000-0887.370280

¹重庆交通大学数学与统计学院, 重庆 400074;²西安工程大学管理学院, 西安 710048;³重庆师范大学数学科学学院, 重庆 401331;⁴云南财经大学数学与统计学院, 昆明 650224

基金项目: 国家自然科学基金(11471059;11431004); 重庆市基础与前沿研究项目(cstc2017jcyjAX0382;cstc2016jcyjA0219);重庆市民生项目(cstc2015shmszx30004);中国博士后科学基金(2015M580774;2016T90837)；重庆市高校创新团队项目(CXTDX201601022)

详细信息

作者简介:
彭再云(1980—)，男，博士, 教授(E-mail: pengzaiyun@126.com);张石生(1934—)，男，教授(通讯作者. E-mail: changss2013@aliyun.com).

中图分类号: O221.1
计量
- 文章访问数: 955
- HTML全文浏览量: 93
- PDF下载量: 451
- 被引次数: 0
出版历程
- 收稿日期: 2016-09-13
- 修回日期: 2017-05-10
- 刊出日期: 2017-07-15

Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

¹College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of Management, Xi’an Polytechnic University, Xi’an 710048, P.R.China;³School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China;⁴School of Statistics and Mathematics,Yunnan University of Finance and Economics, Kunming 650224, P.R.China

Funds: The National Natural Science Foundation of China(11471059;11431004); China Postdoctoral Science Foundation(2015M580774;2016T90837)

摘要

摘要: 提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性.
- E-半连通集 /
- 半严格-G-E-半预不变凸函数 /
- 性质 /
- 非线性规划 /
- 应用
Abstract: A new class of generalized convex functions, namely the semistrict-G-E-semipreinvex functions were proposed, which are a class of very important generalized convex functions and make a true generalization of both the semistrict-G-semipreinvex functions and the semistrict-E-preinvex functions. Firstly, several examples were given to illustrate the existence of semistrict-G-E-semipreinvex functions and the dependence on the related generalized convex functions. Afterwards, the basic characteristics of the semistrict-G-E-semipreinvex functions were discussed. Finally, some applications of the semistrict-G-E-semipreinvex functions in nonlinear programming problems without constraint and with inequality constraints were studied respectively, and some optimality results were obtained; moreover, some examples were given to illustrate the correctness of the obtained results.
- E-semi-connected set /
- semistrict-G-E-semipreinvex function /
- characteristics /
- nonlinear programming /
- application

HTML全文

参考文献(14)

[1]	Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J]. Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
[2]	Weir T, Mond B. Pre-invex functions in multiple objective optimization[J]. Journal of Mathematical Analysis and Applications,1988,136(1): 29-38.
[3]	YANG Xin-min, LI Duan. On properties of preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
[4]	YANG Xin-min, LI Duan. Semistrictly preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
[5]	Yang X Q, CHEN Guang-ya. A class of nonconvex functions and pre-variational inequalities[J]. Journal of Mathematical Analysis and Applications,1992,169(2): 359-373.
[6]	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.(YAN Li-jia, LIU Fu-ping. Strongly preinvex functions[J]. Journal of Chongqing Normal University (Natural Science Edition),2005,22(1): 11-15.(in Chinese))
[7]	彭再云, 李永红. 半严格-G-半预不变凸性与最优化[J]. 应用数学和力学, 2013,34(8): 836-845.(PENG Zai-yun, LI Yong-hong. Semistrict-G-semi-preinvexity and optimization[J]. Applied Mathematics and Mechanics,2013,34(8): 836-845.(in Chinese))
[8]	李科科, 彭再云, 万轩, 等. 严格 G -半预不变凸性及其应用[J]. 重庆师范大学学报(自然科学版), 2015,32(6): 1-8.(LI Ke-ke, PENG Zai-yun, WAN Xuan, et al. The study of strict G -semi-preinvexity and its applications[J]. Journal of Chongqing Normal University (Natural Science),2015,32(6): 1-8.(in Chinese))
[9]	彭再云, 秦南南, 李科科.G-E-半预不变凸型多目标规划的 Wolfe 型对偶[J]. 应用数学学报, 2015,38(6): 1103-1114.(PENG Zai-yun, QIN Nan-nan, LI Ke-ke. Wolf type duality of G-E-semi-preinvex type multiobjective programming problems[J]. Acta Mathematicae Applicatae Sinica,2015,38(6): 1103-1114.(in Chinese))
[10]	Fulga C, Preda V. Nonlinear programming with E -preinvex and local E -preinvex functions[J]. European Journal of Operational Research,2009,192(2): 737-743.
[11]	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.(PENG Zai-yun, ZHOU Xuan-lin, ZHAO Yong. Characteristics and applications of strongly G-preinvex functions[J]. Journal of Chongqing Normal University (Natural Science), 2012,29(4): 12-17.(in Chinese))
[12]	彭再云, 李科科, 张石生. 向量 D-η-Ｅ半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. Semipreinvex vector mappings and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))
[13]	赵映雪. 一类广义凸性及其在最优化理论中的应用[D]. 硕士学位论文. 金华: 浙江师范大学, 2005.(ZHAO Ying-xue. A type of generalized convexity and applications in optimization theory[D]. Master Thesis. Jinhua: Zhejiang Normal University, 2005.(in chinese))
[14]	唐莉萍, 杨新民. 关于D-半预不变凸性的某些新性质[J]. 应用数学和力学, 2015,36(3): 325-331.(TANG Li-ping, YANG Xin-min. A note on some new characteristics of D-semi-preinvexity[J]. Applied Mathematics and Mechanics,2015,36(3): 325-331.(in Chinese))

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 955
HTML全文浏览量: 93
PDF下载量: 451
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究

doi: 10.21656/1000-0887.370280

作者简介:
彭再云(1980—)，男，博士, 教授(E-mail: pengzaiyun@126.com);张石生(1934—)，男，教授(通讯作者. E-mail: changss2013@aliyun.com).

计量

Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

计量

目录

留言板

半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究

doi: 10.21656/1000-0887.370280

作者简介: 彭再云(1980—)，男，博士, 教授(E-mail: pengzaiyun@126.com);张石生(1934—)，男，教授(通讯作者. E-mail: changss2013@aliyun.com).

计量

出版历程

Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

计量

出版历程

目录

作者简介:
彭再云(1980—)，男，博士, 教授(E-mail: pengzaiyun@126.com);张石生(1934—)，男，教授(通讯作者. E-mail: changss2013@aliyun.com).