Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces
Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces
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DOI：
10.1007/s10957-009-9609-1
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发表时间：
2010-04
影响因子：
1.9
通讯作者：
M. Durea;J. Dutta;C. Tammer
中科院分区：
文献类型：
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作者：
M. Durea;J. Dutta;C. Tammer
本文给出了余域中序锥内部为空时向量优化问题的拉格朗日乘子存在性的一些结果。推导我们的断言的主要工具是通过Hiriart-Urruty（Math. Oper. Res. 4：79-97，1979）（所谓的定向距离函数）。此外，我们解释了我们的结果的一些应用向量平衡问题，向量控制逼近问题和无约束向量分式规划问题。
This paper presents some results concerning the existence of the Lagrange multipliers for vector optimization problems in the case where the ordering cone in the codomain has an empty interior. The main tool for deriving our assertions is a scalarization by means of a functional introduced by Hiriart-Urruty (Math. Oper. Res. 4:79–97, 1979) (the so-called oriented distance function). Moreover, we explain some applications of our results to a vector equilibrium problem, to a vector control-approximation problem and to an unconstrainted vector fractional programming problem.