We compare the Fenchel-Moreau second conjugates associated to an arbitrary coupling function φ: X × W → R̄ = [-∞, + ∞] between two sets X and W with the second level set conjugates associated to the same coupling. For a coupling φ: Rn × Rn → R = (-∞, + ∞) that is additively homogeneous in one (or both) of the variables we also compare the first conjugates associated to the same coupling. We give an application to the "min-type" coupling function arising in the study of topical functions.
|Journal||Journal of Convex Analysis|
|Publication status||Published - 2 Jul 2008|
- Generalized conjugation
- Hull operators
- Topical functions