非光滑多目标半无限规划问题的混合型对偶

刘娟; 龙宪军

doi:10.21656/1000-0887.410342

非光滑多目标半无限规划问题的混合型对偶

doi: 10.21656/1000-0887.410342

刘娟,
龙宪军^,

重庆工商大学数学与统计学院，重庆 400067

基金项目:

重庆市教育委员会科学技术研究重点项目（KJZD-K201900801）；重庆市巴渝学者特聘教授专项资助

重庆市基础与前沿研究计划项目（cstc2018jcyjAX0119；cstc2020jcyj-msxmX0053）

国家自然科学基金(面上项目)（11471059）

详细信息

作者简介:
刘娟（1996—），女，硕士生（E-mail: 1016661324@qq.com）;龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

通讯作者:
龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

中图分类号: O221.2
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出版历程
- 收稿日期: 2020-11-11
- 修回日期: 2021-05-05

Mixed Type Duality for Nonsmooth Multiobjective Semi-Infinite Programming Problems

LIU Juan,
LONG Xianjun^,

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China

Funds:

The National Natural Science Foundation of China(11471059)

摘要

摘要: 该文研究了非光滑多目标半无限规划问题的混合型对偶.首先，利用Lagrange函数介绍了非光滑多目标半无限规划混合型对偶的弱有效解和有效解的定义.其次，利用Dini-伪凸性建立了非光滑多目标半无限规划混合型对偶的弱对偶定理、强对偶定理和逆对偶定理.该文所得结果推广了已有文献中的主要结果.
- 多目标半无限规划 /
- Dini-伪凸 /
- 混合型对偶
Abstract: The mixed type duality for nonsmooth multiobjective semi-infinite programming problems was studied. Firstly, by the Lagrange function, the definitions of weakly efficient solutions and efficient solutions to the mixed type duality were introduced. Secondly, by means of the Dini-pseudoconvexity, the weak duality theorems, the strong duality theorems and the converse duality theorems were obtained. The results generalize the main results in previous literatures.
- multiobjective semi-infinite programming /
- Dini-pseudoconvexity /
- mixed type duality

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参考文献(16)

GOBERNA M A, LPEZ M A. Linear Semi-Infinite Optimization[M]. Chichester: Wiley, 1998.

[2]LONG X J, PENG Z Y, WANG X F. Stable Farkas lemmas and duality for nonconvex composite semi-infinite programming problems[J]. Pacific Journal of Optimization,2019,15(2): 295-315.

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[4]KIM D S, SON T Q. Characterizations of solutions sets of a class of nonconvex semi-infinite programming problems[J]. Journal of Nonlinear and Convex Analysis,2011,12(3): 429-440.

[5]PENG Z Y, WANG X F, YANG X M. Connectedness of approximate efficient solutions for generalized semi-infinite vector optimization problems[J]. Set-Valued and Variational Analysis,2019,27(1): 103-118.

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[7]杨玉红, 李飞. 非光滑半无限多目标优化问题的最优性充分条件[J]. 应用数学和力学, 2017,38(5): 526-538.(YANG Yuhong, LI Fei. Sufficient optimality conditions for nonsmooth semi-infinite multiobjective optimization problems[J]. Applied Mathematics and Mechanics,2017,38(5): 526-538.(in Chinese))

[8]GULATI T R, ISLAM M A. Sufficiency and duality in multiobjective programming involving generalized F-convex functions[J]. Journal of Mathematical Analysis and Applications,1994,183(1): 181-195.

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[10]TUNG L T. Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions[J]. Numerical Functional Analysis and Optimization,2020,62(1): 67-91.

[11]SON T Q, KIM D S. ε-mixed type duality for nonconvex multiobjective programs with an infinite number of constraints[J]. Journal of Global Optimization,2013,57(2): 447-465.

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非光滑多目标半无限规划问题的混合型对偶

doi: 10.21656/1000-0887.410342

作者简介:
刘娟（1996—），女，硕士生（E-mail: 1016661324@qq.com）;龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

通讯作者:
龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

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Mixed Type Duality for Nonsmooth Multiobjective Semi-Infinite Programming Problems

计量

目录

留言板

非光滑多目标半无限规划问题的混合型对偶

doi: 10.21656/1000-0887.410342

作者简介: 刘娟（1996—），女，硕士生（E-mail: 1016661324@qq.com）;龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

通讯作者: 龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

计量

出版历程

Mixed Type Duality for Nonsmooth Multiobjective Semi-Infinite Programming Problems

计量

出版历程

目录

作者简介:
刘娟（1996—），女，硕士生（E-mail: 1016661324@qq.com）;龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.

通讯作者:
龙宪军（1980—），男，教授，博士（通讯作者. E-mail: xianjunlong@ctbu.edu.cn）.