Scalarization and Optimality Conditions for Vector Equilibrium Problems via Improvement Sets in Real Linear Spaces
首发时间:2018-09-27
Abstract:In this paper, we study vector equilibrium problems with the ordering relations defined via improvementsets in real linear spaces without assuming any topology. We deal with efficient solutions, weak efficient solutions, Benson and Henig proper efficient solutions. The linear scalarization characterizations of these solutions are established, moreover, optimization conditions via Lagrange multiplier rulers for vector equilibrium problems with constraints are also obtained. Our results generalized the corresponding ones in the literature.
keywords: Vector equilibrium problems Improvement set Linear scalarization Lagrange multiplier rules Optimality conditions
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实线性空间中基于改进集的向量平衡问题的标量化与最优性条件
摘要:本文在无拓扑结构的实线性空间中研究由改进集来定义序关系的向量平衡问题。主要处理模型的有效解、弱有效解、Benson和Henig真有效解。建立了这些解的线性标量化刻画,并在显式约束下得到了由Lagrange乘子法则刻画的最优性条件。所得结果推广了有关文献中的对应结论。
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