A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory |
| |
| Authors: | Andreas H Hamel |
| |
| Institution: | (1) Department of Operations Research and Financial Engineering, Princeton University, Sherrerd Hall, Charlton Street, Princeton, NJ, USA |
| |
| Abstract: | 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.
|
| |
| Keywords: | Set order relations Legendre– Fenchel conjugate Moreau– Fenchel theorem Set-valued function Conlinear space Set-valued risk measure |
| 本文献已被 SpringerLink 等数据库收录！ |
|
