Maximizing the Bregman divergence from a Bregman family
The problem to maximize the information divergence from an exponential family is generalized to the setting of Bregman divergences and suitably defined Bregman families.
Monotone Valuations on the Space of Convex Functions
We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
More than first-order developments of convex functions: primal-dual relations.