向量优化问题中的弱S-有效解

doi:10.15960/j.cnki.issn.1007-6093.2016.01.005

运筹学学报

向量优化问题中的弱S-有效解

郭辉^1,* 白延琴²

1. 重庆师范大学数学科学学院, 重庆 401331; 2. 上海大学理学院, 上海 200444

收稿日期:2015-03-20 出版日期:2016-03-15 发布日期:2016-03-15
通讯作者: 郭辉 guoguofly@163.com
基金资助:

国家自然科学基金重点项目(No. 11431004), 国家自然科学基金(Nos. 11301574,11271391), 重庆市教委科学技术研究项目(No. KJ1500310)

Weak S-efficient solution of vector optimization

GUO Hui^1,* BAI Yanqin²

1. College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China; 2. College of Science, Shanghai University, Shanghai 200444, China

Received:2015-03-20 Online:2016-03-15 Published:2016-03-15

摘要/Abstract

摘要：

在局部凸拓扑线性空间中, 提出了集值向量优化问题的弱S-有效解和S-次似凸性概念. 在S-次似凸性假设下建立了择一性定理, 并利用择一性定理建立了弱S-有效解的标量化定理. 此外, 通过几个具体例子解释了主要结果.

关键词: 向量优化, S-次似凸, 弱S-有效解, 择一性定理, 标量化定理

Abstract:

In this paper, we introduce the concept of weak S-optimal solution and S-subconvexlikeness of vector optimization with set-valued maps and obtain an alternative theorem in a real locally Hausdorff topological vector space. Furthermore, under the assumption of S-subconvexlikeness, we establish scalarization theorem for weak S-efficient solution. We also give some examples to illustrate the main results.

Key words: vector optimization, S-subconvexlikeness, weak S-efficient solution, alternative theorem, scalarization theorem

郭辉, 白延琴. 向量优化问题中的弱S-有效解[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.005.

GUO Hui, BAI Yanqin. Weak S-efficient solution of vector optimization[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.005.

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向量优化问题中的弱S-有效解

Weak S-efficient solution of vector optimization

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