| Asplund空间中非凸向量均衡问题近似解的最优性条件 |
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| 引用本文： | 龙宪军.Asplund空间中非凸向量均衡问题近似解的最优性条件[J].数学物理学报(A辑),2014,34(3):593-602. |
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| 作者姓名： | 龙宪军 |
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| 作者单位： | 重庆工商大学数学与统计学院 重庆 400067 |
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| 基金项目： | 国家自然科学基金(11001287, 71271226)、重庆市自然科学基金(CSTC 2010BB9254, CSTC 2012jjA00039)和重庆市教委科技研究项目(KJ100711)资助 |
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| 摘 要： | 在Asplund空间中,研究了非凸向量均衡问题近似解的最优性条件.借助Mordukhovich次可微概念,在没有任何凸性条件下获得了向量均衡问题εe-拟弱有效解,εe-拟Henig有效解,εe-拟全局有效解以及εe-拟有效解的必要最优性条件.作为它的应用,还给出了非凸向量优化问题近似解的最优性条件.
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| 关 键 词： | 非凸向量均衡问题 近似解 最优性条件 Mordukhovich次可微. |
| 收稿时间： | 2012-09-18 |
| 修稿时间： | 2013-04-16 |
Optimality Conditions for Approximate Solutions on NonconvexVector Equilibrium Problems in Asplund Spaces |
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| LONG Xian-Jun.Optimality Conditions for Approximate Solutions on NonconvexVector Equilibrium Problems in Asplund Spaces[J].Acta Mathematica Scientia,2014,34(3):593-602. |
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| Authors: | LONG Xian-Jun |
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| Institution: | College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 40006 |
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| Abstract: | The purpose of this paper is to study approximate solutions for the vector equilibrium problem in Asplund spaces without any convexity assumption. We obtain optimality conditions for εe-quasi weakly efficient solutions, εe-quasi Henig efficient solutions, εe-quasi globally efficient solutions and εe-quasi efficient solutions to vector equilibrium problems
by the Mordukhovich subdifferential. As applications of our results, we derive some optimality conditions for nonconvex vector optimization problems. |
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| Keywords: | Nonvector vector equilibrium problemzz Approximate solutionzz Optimality conditionzz Mordukhovich subdifferentialzz |
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