Éditeur(s) : HAL CCSD
Résumé : International audience
The author proposes a generalized proximal method for solving an equilibrium problem which consists in finding x 2 K such that F(x, y) 0, for all y 2 K, where K is a nonempty, convex and closed set of a real Hilbert space X, and F:K ×K !Ris a given bifunction with F(x, x) = 0 for all x 2 K. The weak convergence of the sequence generated by the method is proved under the assumptions of monotonicity and convexity, with respect to the second argument y (for every fixed x 2 K), of the bifunction F. Replacing the assumption of monotonicity with the one of strong monotonicity on F, a strong convergence result is obtained. A second strong convergence theorem is proved under the hypotheses of monotonicity and a new assumption of "co-Lipschitz continuity at 0" of the operator F. Applications to convex optimization, to the problem of finding a zero of a maximal monotone operator and to Nash equilibria problems are provided.
Journal of Natural Geometry

hal-00773194
https://hal.univ-antilles.fr/hal-00773194

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 : In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.
https://hal.univ-antilles.fr/hal-00783905

hal-00783905
https://hal.univ-antilles.fr/hal-00783905
https://hal.univ-antilles.fr/hal-00783905/document
https://hal.univ-antilles.fr/hal-00783905/file/10.1.1.165.7044.pdf

Éditeur(s) : HAL CCSD IOP Publishing
Résumé : International audience
We extend the notion of central charge superspace to the case of local supersymmetry. Gauged central charge transformations are identified as diffeomorphisms on the same footing as spacetime diffeomorphisms and local supersymmetry transformations. Given the general structure we then proceed to the description of a particular vector-tensor supergravity multiplet of 24 + 24 components, identified by means of rather radical constraints.
ISSN: 0264-9381

hal-00769899
https://hal.univ-antilles.fr/hal-00769899
DOI : 10.1088/0264-9381/16/5/311

Éditeur(s) : HAL CCSD
Résumé : International audience
In this note we show that the splitting scheme of Passty [13] as well as the barycentric-proximal method of Lehdili & Lemaire [8] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we generalize a convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results of Passty and Lehdili & Lemaire when the pointwise sum of the involved operators in maximal monotone.
Studies in Computational Mathematics

hal-00778164
https://hal.univ-antilles.fr/hal-00778164
DOI : 10.1016/S1570-579X(01)80022-7