Continuity concepts for set-valued functions and a fundamental duality formula for set-valued optimization
Continuity concepts for set-valued functions and a fundamental duality formula for set-valued optimization
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DOI：
10.1016/j.jmaa.2012.08.019
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发表时间：
2013-01
影响因子：
1.3
通讯作者：
F. Heyde;Carola Schrage
中科院分区：
文献类型：
--
作者：
F. Heyde;Carola Schrage
在过去的几年里，对于映射到预定拓扑向量空间上闭子集集的集值函数的共轭对偶性理论得到了发展。对于标量对偶理论，凸函数的连续性起着重要的作用。对于集值映射，存在不同的连续性概念。我们将比较图像空间是预定拓扑向量空间的上闭子集的集合的特殊情况下最流行的结果，并分析哪些结果可以从扩展实值情况中传达出来。此外，我们在考虑正则性条件下，利用连续性概念的最弱，给出了集值优化的基本对偶公式。
Over the past few years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space has been developed. For scalar duality theory, continuity of convex functions plays an important role. For set-valued maps, different notions of continuity exist. We will compare the most prevalent ones for the special case where the image space is the set of upper closed subsets of a preordered topological vector space and analyze which of the results can be conveyed from the extended real-valued case. Moreover, we present a fundamental duality formula for set-valued optimization, using the weakest of the continuity concepts under consideration for a regularity condition.