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A characterization of closed convex sets possessing a barrier cone with a nonempty interior is achieved. As a consequence, we describe all the proper extended-valued functionals for which the domain of their Fenchel conjugate has a nonempty interior. We end up the paper by giving an application to the study of the stability of the solution set of a… (More)

- S. Adly, E. Ernst, M. Théra, Albert Thomas, SAMIR ADLY
- 2003

We characterize in a reflexive Banach space all the closed convex sets ensures the closedness of the algebraic difference ¡ ¨ for all closed convex sets¨. We also answer a closely related problem: determine all the pairs ¡ , ¨ of closed convex sets containing no lines such that the algebraic difference of any sufficiently small uniform perturbation of ¢ ¡… (More)

- Samir Adly, Emil Ernst, Michel Théra
- 2000

When the subdifferential sum rule formula holds for the indicator functions ι C and ι D of two closed convex sets C and D of a locally convex space X, the pair (C, D) is said to have the strong conical hull intersection property (the strong CHIP). The specification of a well-known theorem due to Moreau to the case of the support functionals σ C and σ D… (More)

The concept of continuous set has been used in finite dimension by Gale and Klee and recently by Auslender and Coutat. Here, we introduce the notion of slice-continuous set in a general reflexive Ba-nach space and we show that the class of such sets can be viewed as a subclass of the class of continuous sets. Further, we prove that every non constant… (More)

This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is… (More)

- EMIL ERNST, MICHEL VOLLE
- 2011

This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee's boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we are able to characterize… (More)

- EMIL ERNST
- 2011

Given x 0 , a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any convex function f : C → R is upper semi-continuous at x 0 , and (ii) C is polyhedral at x 0. In the particular setting of closed convex mappings and Fσ domains, we prove that any closed convex function f : C → R is continuous at… (More)

- EMIL ERNST
- 2010

The main concern of this article is to study Ulam stability of the set of ε-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space X, when the objective function is subjected to small perturbations (in the sense of Attouch & Wets). More precisely, we characterize the class all proper lower semicontinuous… (More)