集合最优化问题的Lagrange对偶

李毛亲; 李杉林

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集合最优化问题的Lagrange对偶

应用基础研究 | 更新时间：2026-09-14

- 集合最优化问题的Lagrange对偶
- Lagrangian Duality for Set Optimization Problem
- 中北大学学报（自然科学版） 2011年32卷第4期页码：392-397
- 作者机构：
  
  台州学院数学系,浙江,台州,317000
- 作者简介：
- 基金信息：
  
  山西省留学回国人员基金资助项目(2010087);浙江省台州学院培育基金资助项目(2010PY112011PY06)
- DOI：
  中图分类号：
- 纸质出版：2011
- 稿件说明：
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李毛亲, 李杉林. 集合最优化问题的Lagrange对偶[J]. 中北大学学报（自然科学版）, 2011,32(4):392-397.

李毛亲, 李杉林. Lagrangian Duality for Set Optimization Problem[J]. 2011, 32(4): 392-397.
李毛亲, 李杉林. 集合最优化问题的Lagrange对偶[J]. 中北大学学报（自然科学版）, 2011,32(4):392-397. DOI：

李毛亲, 李杉林. Lagrangian Duality for Set Optimization Problem[J]. 2011, 32(4): 392-397. DOI：

摘要

在偏序拓扑线性空间

讨论了具有集值映射的最优化问题的L agrange对偶和鞍点问题.该最优化问题解的判别依赖于目标空间集合之间的下关系.对于给定的具有线性乘子的L agrange集值映射

在公理化对偶的框架下

得到了弱对偶定理;在CY-次类凸的条件下得到了强对偶定理.给出了鞍点存在的必要条件和充分条件

同时通过鞍点得到了集合最优化问题解的存在性条件.

Abstract

In partially ordered topological linear space

Lagrangian duality and saddle points of the set optimization problem were concerned

where the solutions to the problem are identified by set criterion.For a given Lagrangian map with linear multiplier

a weak duality theorem was obtained under the frame of axiomatic duality principles;and a strong duality theorem was developed under the condition of CY-subconvexlikeness.A sufficient condition and a necessary condition of the existence of saddle points were given.Through these saddle points

the existence conditions of solution to the set optimization problem were presented.

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references

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