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浙江大学学报(理学版)
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集值向量均衡问题近似有效解的最优条件
孟旭东(1982—),ORCID:https://orcid.org/0000-0002-0465-8323,男,硕士,副教授,主要从事向量均衡与向量优化理论研究,E-mail:mxudongm@163.com.
Optimality conditions of approximate efficient solutions to set-valued vector equilibrium problems
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摘要: 分析实局部凸Hausdorff拓扑向量空间一类具约束集值向量均衡问题的近似有效解,讨论其有效解和近似有效解的关系。在近似锥-次类凸集值映射概念的基础上,运用凸集分离定理,建立了有效解和近似有效解的最优条件。在广义凸性假设条件下,借助相应的分析方法,得到集值向量均衡问题近似有效解的Kuhn-Tucker型和Lagrange型的最优充要条件。
Abstract: In this paper,a kind of approximate efficient solutions to set-valued vector equilibrium problems with constraints is analyzed in real locally convex Hausdorff topological vector spaces,and the relationship between the efficient solutions and the approximate efficient solutions is discussed.Based on the concept of nearly cone-subconvexlike set-valued mapping,the optimality conditions of efficient solutions and approximate efficient solutions are established by applying the separation theorem for convex sets.Using analytic method,under the assumption of generalized convexity,the optimality necessary and sufficient conditions for both the Kuhn-Tucker-type and Lagrange-type approximate efficient solutions to the set-valued vector equilibrium problems are obtained.
收稿日期: 2019-12-11 出版日期: 2016-12-30
基金资助: 国家自然科学基金资助项目(11201216);江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614).
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引用本文:

孟旭东. 集值向量均衡问题近似有效解的最优条件[J]. 浙江大学学报(理学版), 10.3785/j.issn.1008-9497.2021.04.007.

MENG Xudong. Optimality conditions of approximate efficient solutions to set-valued vector equilibrium problems. Journal of ZheJIang University(Science Edition), 10.3785/j.issn.1008-9497.2021.04.007.

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http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2021.04.007        http://www.zjujournals.com/sci/CN/Y0/V/I/1

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