| 向量优化问题中的弱S-有效解 |
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| 引用本文： | 郭辉,白延琴. 向量优化问题中的弱S-有效解[J]. 运筹学学报, 2016, 20(1): 54-60. DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.005 |
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| 作者姓名： | 郭辉 白延琴 |
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| 作者单位： | 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 |
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| 基金项目： | 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) |
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| 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.
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| 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 |
| 收稿时间： | 2015-03-20 |
Weak S-efficient solution of vector optimization |
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| GUO Hui,BAI Yanqin. Weak S-efficient solution of vector optimization[J]. OR Transactions, 2016, 20(1): 54-60. DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.005 |
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| Authors: | GUO Hui BAI Yanqin |
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| Affiliation: | 1. College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China; 2. College of Science, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper, we introduce the concept of weak S-optimal solution and S-subconvexlikeness of vector optimization with set-valued mapsand 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. |
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| Keywords: | vector optimization S-subconvexlikeness weak S-efficient solution alternative theorem scalarization theorem |
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