Éditeur(s) : HAL CCSD IOP Publishing
Résumé : International audience
Based on the very recent work by Censor and Segal (2009 J. Convex Anal. 16 587-600) and inspired by Xu (2006 Inverse Problems 22 2021-34) and Yang (2004 Inverse Problems 20 1261-6), we investigate an algorithm for solving the split common fixed-point problem for the class of demicontractive operators in a Hilbert space. Our results improve and/or develop previously discussed feasibility problems and related algorithms. It is worth mentioning that the convex feasibility formalism is at the core of the modeling of many inverse problems and has been used to model significant real-world problems, for instance, in sensor networks, in radiation therapy treatment planning, in computerized tomography and data compression, see Censor et al (2006 Phys. Med. Biol. 51 2353-65) and Combettes (1996 Adv. Imaging Electron. Phys. 95 155-270) and references therein.
ISSN: 0266-5611

hal-00778174
https://hal.univ-antilles.fr/hal-00778174
DOI : 10.1088/0266-5611/26/5/055007

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Based on the very recent work by Censor-Gibali-Reich (http://arxiv.org/abs/1009.3780), we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnosel'skii-Mann Theorem for averaged operators, we analyze an algorithm for solving new split monotone inclusions under weaker conditions. Our weak convergence results improve and develop previously discussed Split Variational Inequality Problems, feasibility problems and related problems and algorithms.
ISSN: 0022-3239

hal-00776651
https://hal.univ-antilles.fr/hal-00776651
DOI : 10.1007/s10957-011-9814-6

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Let H1,H2,H3 be real Hilbert spaces, let C⊂H1, Q⊂H2 be two nonempty closed convex level sets, let A:H1→H3, B:H2→H3 be two bounded linear operators. Our interest is in solving the following new convex feasibility problem Find x∈C,y∈Q such that Ax=By, which allows asymmetric and partial relations between the variables x and y. In this paper, we present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution of (1.1). The interest of RACQA is that we just need projections onto half-spaces, thus making the relaxed CQ-algorithm implementable. Note that, by taking B=I, in (1.1), we recover the split convex feasibility problem originally introduced in Censor and Elfving (1994) [13] and used later in intensity-modulated radiation therapy (Censor et al. (2006) [11]). We also recover the relaxed CQ-algorithm introduced by Yang (2004) [8] by particularizing both B and a given parameter.
ISSN: 0362-546X

hal-00776638
https://hal.univ-antilles.fr/hal-00776638
DOI : 10.1016/j.na.2012.11.013

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Based on the very recent work by Censor and Segal (2009), and inspired by Xu (2006), Zhao and Yang (2005) , and Bauschke and Combettes (2001), we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms.
ISSN: 0362-546X

hal-00776645
https://hal.univ-antilles.fr/hal-00776645
DOI : 10.1016/j.na.2011.03.041

Éditeur(s) : HAL CCSD
Résumé : The convex feasibility problem (CFP) is to find a member of the intersection of finitely many closed convex sets in Euclidean space. When the intersection is empty, one can minimize a proximity function to obtain an approximate solution to the problem. The split feasibility problem (SFP) and the split equality problem (SEP) are generalizations of the CFP. The approximate SFP (ASFP) and approximate SEP (ASEP) involve finding only approximate solutions to the SFP and SEP, respectively. We present here the SSEA, a simultaneous iterative algorithm for solving the ASEP. When this algorithm is applied to the ASFP it resembles closely, but is not equivalent to, the CQ algorithm. The SSEA involves orthogonal projection onto the given closed convex sets. The relaxed SSEA (RSSEA) is an easily implementable variant of the SSEA that uses orthogonal projection onto half-spaces at each step to solve the SEP. The perturbed version of the SSEA (PSSEA) is similar to the RSSEA, but uses orthogonal projection onto a sequence of epi-convergent closed convex sets.
https://hal.univ-antilles.fr/hal-00776640

Droits : info:eu-repo/semantics/OpenAccess
hal-00776640
https://hal.univ-antilles.fr/hal-00776640
https://hal.univ-antilles.fr/hal-00776640/document
https://hal.univ-antilles.fr/hal-00776640/file/CBAM10.pdf

Éditeur(s) : HAL CCSD
Résumé : International audience
BACKGROUND: The aim of this systematic review was to evaluate and compare the pros and cons of using living donors or brain-dead donors in uterus transplantation programs, 2 years after the first worldwide live birth after uterus transplantation. METHODS: The Medline database and the Central Cochrane Library were used to locate uterine transplantation studies carried out in human or nonhuman primates. All types of articles (case reports, original studies, meta-analyses, reviews) in English or French were considered for inclusion. RESULTS: Overall, 92 articles were screened and 44 were retained for review. Proof of concept for human uterine transplantation was demonstrated in 2014 with a living donor. Compared with a brain-dead donor strategy, a living donor strategy offers greater possibilities for planning surgery and also decreases cold ischemia time, potentially translating into a higher success rate. However, this approach poses ethical problems, given that the donor is exposed to surgery risks but does not derive any direct benefit. A brain-dead donor strategy is more acceptable from an ethical viewpoint, but its feasibility is currently unproven, potentially owing to a lack of compatible donors, and is associated with a longer cold ischemia time and a potentially higher rejection rate. CONCLUSIONS: The systematic review demonstrates that uterine transplantation is a major surgical innovation for the treatment of absolute uterine factor infertility. Living and brain-dead donor strategies are not mutually exclusive and, in view of the current scarcity of uterine grafts and the anticipated future rise in demand, both will probably be necessary.
Transplantation

hal-01447062
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01447062
DOI : 10.1097/TP.0000000000001481
PUBMED : 27607535

Éditeur(s) : Université des Antilles Études caribéennes
Résumé : La Martinique est actuellement en proie un taux de chômage chronique élevé et une augmentation constante du coût de la nourriture et des autres produits essentiels. La catastrophe écologique s’ajoute à ce problème sociétal avec la contamination par la chlordécone d'environ un tiers de la surface de la terre et les eaux environnantes de cette île. La chlordécone est extrêmement toxique et récalcitrante, son utilisation fut interdite aux Etats-Unis dès 1979 mais elle fut utilisée continuellement jusqu'en 1993. L’agriculture alternative est un moyen pratique pour atténuer le malaise social profond résultant d’un taux de chômage chroniquement élevé et d’une dépendance totale envers les couteuses importations alimentaires de la France métropolitaine. L'un des objectifs de base de cette approche serait de ne pas utiliser de produits chimiques. La culture de certaines plantes solanacées comestibles, comme le poivron, semble être possible dans cet environnement avec l’installation de serres semi-ouvertes, dans lesquelles la lumière naturelle, les précipitations et les températures chaudes toute l'année sont abondantes. Dans cette perspective, l'empreinte carbone de telles productions réalisées en Martinique pourraient être livrées au Royaume-Uni avec une empreinte carbone sensiblement inférieure à celle de poivrons cultivés dans des serres chauffées autonomes d’Europe.
Martinique is currently beset by, among other things, chronic high unemployment rate and steadily rising cost of food and other life essentials. Overlaying this societal problem is the continuing ecological disaster of chlordecone contamination of about 1/3 of the land surface, and surrounding waters. Chlordecone is extremely toxic and recalcitrant; its use was banned in the USA in 1979, but it was used continually until 1993. Alternative agriculture is a practicable means to alleviate the deep social unrest arising from chronically high unemployment rate and near total dependency on costly food imports from metropolitan France. One of the basics aims of this approach would be the zero use of synthetic chemicals for pest-and weed-control for all crops. Cropping of certain edible Solanaceae fruits, viz, bell pepper, appears to be feasible under a semi-open greenhouse environment, in which natural sunlight, rainfall and warm year-round temperatures would be deployed maximally. The carbon footprint of this prospective Martinique produce delivered to the UK might be substantially lower than that of bell peppers grown in stand-alone heated greenhouses in mainland Europe.
Martinique

Droits : info:eu-repo/semantics/openAccess
urn:doi:10.4000/etudescaribeennes.6710
http://journals.openedition.org/etudescaribeennes/6710

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
We study the convergence of a variable version of the Krasnoselski-Mann algorithm applied to a primal dual fixed point problem. The link with Spingarn's partial inverse method is made, and an application to feasibility problems and mathematical programming is also proposed.
ISSN: 0163-0563

hal-00779984
https://hal.univ-antilles.fr/hal-00779984
DOI : 10.1080/01630560902987436