Maximal monotone relations and the second derivatives of nonsmooth functions
Midpoint convex functions majorized by midpoint concave functions.
Midpoint convex functions majorized by midpoint concave functions. (Short Communication).
Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev inequalities...
Mond-Weir duality in vector programming with generalized invex functions on differentiable manifolds.
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.
Multifunctions with selections of convex and concave type.
Multivariate version of a Jensen-type inequality.