New generalized convexity notion for set-valued maps and application to vector optimization
New generalized convexity notion for set-valued maps and application to vector optimization
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DOI：
10.1007/s10957-004-1716-4
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发表时间：
2005-04-01
影响因子：
1.9
通讯作者：
Sach, PH
中科院分区：
文献类型：
--
作者：
Sach, PH
在本文中，我们引入了一个新的广义凸性概念的集值映射，所谓的ic锥类凸性，并使用它作为主要工具，推导出一个替代定理和必要条件的有效，弱有效，和本森真有效的解决方案的问题，集值映射的集值约束。我们的结果对一类比文献[1]中所考虑的问题更广泛的优化问题是有效的。1-6并推广了这些文献的相应结果。
In this paper, we introduce a new generalized convexity notion for set-valued maps, called ic-cone-convexlikeness, and use it as the main tool to derive an alternative theorem and necessary conditions for efficient, weakly efficient, and Benson properly efficient solutions of the problem of minimizing a set-valued map subject to set-valued constraints. Our results are valid for a class of optimization problems broader than that of the problems considered in Refs. 1-6 and generalize the corresponding results of these references.