Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets
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摘要: 在局部凸空间中,研究了带约束集值向量均衡问题的最优性条件.首先,利用改进集引进了带约束集值向量均衡问题的E-Henig真有效解和E-超有效解的概念.其次,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-Henig真有效解的充分必要性条件.最后,在邻近E-次似凸的假设下,建立了带约束集值向量均衡问题的E-超有效解的必要性条件.
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关键词:
- 改进集 /
- 邻近E-次似凸 /
- E-Henig真有效解 /
- E-超有效解 /
- 最优性条件
Abstract: The optimality conditions for setvalued vector equilibrium problems with constraints were investigated in locally convex spaces. Firstly, the concepts of the E-Henig properly efficient solution and the E-super efficient solution to the setvalued vector equilibrium problems with constraints involving improvement sets were introduced. Secondly, under the assumption of the nearly E-subconvexlikeness, the sufficient and necessary conditions for the setvalued vector equilibrium problem with constraints were established in the sense of the E-Henig proper efficiency. Finally, based on the nearly E-subconvexlikeness, the necessary conditions for the setvalued vector equilibrium problem with constraints were obtained in the sense of the E-super efficiency. -
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