A Set-Valued Ekeland's Variational Principle in Vector Optimization
A Set-Valued Ekeland's Variational Principle in Vector Optimization
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DOI：
10.1137/060672868
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发表时间：
2008-03
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影响因子：
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通讯作者：
C. Gutiérrez;B. Jiménez;V. Novo
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文献类型：
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作者：
C. Gutiérrez;B. Jiménez;V. Novo
本文讨论向量优化问题的Ekeland变分原理。通过使用一个集值度量，一个集值扰动映射，和一个基于标量化的锥有界性概念，我们引入了一个原始的方法来扩展著名的标量Ekeland的原则，向量值映射。作为这种方法的结果，我们得到一个Ekeland的变分原理，不依赖于任何近似的效率概念。这一结果与文献中证明的其他Ekeland原理有关，并且有限维情况通过我们在[Math. Methods Oper.]中引入的$\vareps $-有效性概念来发展。结果：64（2006），pp. 165-185; SIAM J. Optim.，17（2006），pp. 688-710]。
This paper deals with Ekeland's variational principle for vector optimization problems. By using a set-valued metric, a set-valued perturbed map, and a cone-boundedness concept based on scalarization, we introduce an original approach to extending the well-known scalar Ekeland's principle to vector-valued maps. As a consequence of this approach, we obtain an Ekeland's variational principle that does not depend on any approximate efficiency notion. This result is related to other Ekeland's principles proved in the literature, and the finite-dimensional case is developed via an $\varepsilon$-efficiency notion that we introduced in [Math. Methods Oper. Res., 64 (2006), pp. 165-185; SIAM J. Optim., 17 (2006), pp. 688-710].