Éditeur(s) : HAL CCSD Academic Publishing Ltd
Résumé : International audience
An approximate procedure for solving the problem of nding a zero of a maximal monotone operator is proposed and its convergence is established under various conditions. More precisely, it is shown that this method weakly converges under natural assumptions and strongly converges provided that either the inverse of the involved operator is Lipschitz continuous around zero or the interior of the solution set is nonempty. A particular attention is given to the convex minimization case. AMS Subject Classication : Primary, 90C ; Secondary, 49M45, 65C.
ISSN: 1311-8080

hal-00779255
https://hal.univ-antilles.fr/hal-00779255
https://hal.univ-antilles.fr/hal-00779255/document
https://hal.univ-antilles.fr/hal-00779255/file/10.1.1.13.4261_3_.pdf

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 Springer Verlag (Germany)
Résumé : International audience
Naegleria fowleri is found in most geothermal baths of Guadeloupe and has been responsible for the death of a 9-year-old boy who swam in one of these baths in 2008. We wanted to determine the origin for the presence of this amoeba in the water.Water samples were taken at the origin of the geothermal sources and at the arrival in the baths. After filtration, cultures were made and the number of Naegleria present was determined using the most probable number method. Soil samples collected in the proximity of the baths were also tested for the presence of thermophilic amoebae. The species identification was obtained by PCR. During three consecutivemonths, no Naegleria could be found at the origin of any geothermal source tested. In contrast, N. fowleri was isolated at least once in all baths at the arrival of the water, except one. Thermophilic amoebae could be found in each soil sample, especially near the baths located at a lower altitude, but N. fowleri was only isolated near two baths, which were also the baths most often contaminated with this species. So it appears that the contamination of the water with N. fowleri occurs after emerging from the geothermal source when the water runs over the soil. Therefore, it should be possible to reduce the concentration of N. fowleri in thegeothermal baths of Guadeloupe to for example less than 1 N. fowleri/10 L by installing a pipeline between the geothermal sources and the baths and by preventing flooding water from entering the baths after rainfall. By taking these measures, we were able to eliminate N. fowleri from a poollocated inside a reeducation clinic.
ISSN: 0932-0113

pasteur-01136739
https://hal-riip.archives-ouvertes.fr/pasteur-01136739
DOI : 10.1007/s00436-014-4197-x.
PUBMED : 25352239

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The aim of this paper is twofold. First, it is to extend the sensitivity analysis framework, developed recently for variational inequalities, to mixed equilibrium problems. The second is to propose iterative methods for solving this kind of problems. In the process, we establish an equivalence between an extended version of Wiener-Hopf equations and the given problems relying on a generalization of the Yosida approximation notion. Our results generalize results obtained for optimization, variational inequalities, complementarity problems, and problems of Nash equilibria.
ISSN: 0898-1221

hal-00779234
https://hal.univ-antilles.fr/hal-00779234
DOI : 10.1016/S0898-1221(02)00218-3

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