Continuity properties of projection operators.
Differentiability of convex functions on a Banach space with smooth bump function.
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular...
Entropic Projections and Dominating Points
Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations...
Epiconvergence and -subgradients of convex functions.
Equilibrium analysis of Kantorovich spaces.
Examples of convex functions and classifications of normed spaces.
Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems
In this paper, which is an extension of [4], we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions.
Extensions of convex functionals on convex cones
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
External approximation of first order variational problems via W-1,p estimates
Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving norms obtained by Nečas and on the general framework of Γ-convergence theory.
From Eckart and Young approximation to Moreau envelopes and vice versa
In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.
Generalized centers of finite sets in Banach spaces.
Generalized vector equilibrium-like problems without pseudomonotonicity in Banach spaces.
Kantorovich spaces and optimization.
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Lasry-Lions regularization and a lemma of Ilmanen
Levitin-Polyak well-posedness for equilibrium problems with functional constraints.
Local and global -cone porosity
Logarithmic functional mean in convex analysis.