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
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- 文章访问数: 1185
- HTML全文浏览量: 160
- PDF下载量: 452
- 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

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参考文献(14)

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文章访问数: 1185
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PDF下载量: 452
被引次数: 0

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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).

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

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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).