Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
Recently Auslender & Crouzeix introduced a well-behaved asymptotical notion for convex functions. The aim of this work is to extend this notion to the saddle case
ISSN: 0163-0563

hal-00773195
https://hal.univ-antilles.fr/hal-00773195
DOI : 10.1080/01630569708816806

Éditeur(s) : HAL CCSD
Résumé : International audience
We start from a basic version of the Hahn-Banach theorem, of which we provide a proof based on Tychonoff's theorem on the product of compact intervals. Then, in the first section, we establish conditions ensuring the existence of affine functions lying between a convex function and a concave one in the setting of vector spaces -- this directly leads to the theorems of Hahn-Banach, Mazur-Orlicz and Fenchel. In the second section, we caracterize those topological vector spaces for which certain convex functions are continuous -- this is connected to the uniform boundedness theorem of Banach-Steinhaus and to the closed graph and open mapping theorems of Banach. Combining both types of results readily yields topological versions of the theorems of the first section.
Nonconvex Optim. Appl.
Erice, Italy

Droits : info:eu-repo/semantics/OpenAccess
hal-00699215
https://hal.archives-ouvertes.fr/hal-00699215
https://hal.archives-ouvertes.fr/hal-00699215/document
https://hal.archives-ouvertes.fr/hal-00699215/file/M_NonconvexOptimAppl98.pdf