A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory
A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory
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DOI：
10.1007/s11228-009-0109-0
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发表时间：
2009-04
影响因子：
1.6
通讯作者：
A. Hamel
中科院分区：
文献类型：
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作者：
A. Hamel
证明了值在预序可分局部凸空间幂集中的真闭凸函数是其集值仿射子式的点态上确界。引入了集值函数Legendre-Fenchel共轭的新概念，证明了一个Moreau-Fenchel定理.给出了例子和应用，其中包括集值凸风险度量的对偶表示定理。
It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre–Fenchel conjugates for set-valued functions is introduced and a Moreau–Fenchel theorem is proven. Examples and applications are given, among them a dual representation theorem for set-valued convex risk measures.