A Fenchel-Rockafellar duality theorem for set-valued optimization

作者：Hamel Andreas H^*

来源：Optimization, 2011, 60(8-9): 1023-1043.

DOI：10.1080/02331934.2010.534794

• set relations
• duality
• Fenchel conjugate
• Fenchel-Rockafellar theorem
• set-valued function
• conlinear space
• supremal convolution
• set-valued risk measures

A duality theorem of the Fenchel-Rockafellar type for set-valued optimization problems is presented along with a result for the conjugate of the sum of two set-valued functions and a chain rule. The underlying solution concepts rely on order complete lattices of sets defined via set relations. Set-valued replacements for linear operators are used as dual variables, for example in order to define Fenchel conjugates for set-valued functions. An application to mathematical finance is given.

• 出版日期2011