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
Résumé : International audience
In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general noncon vex quasi variational inequalities and the xed point problems. This alternative equivalent formulation is used to study the existence of a solution of the general nonconvex quasi variational inequalities. Using these equivalent for-mulations, we suggest and analyze a wide class of new extragradient methods for solving the general nonconvex quasi variational inequalities. Convergence criteria of these new iterative methods is considered under some suitable conditions.
Bulletin of Mathematical Analysis and Applications

hal-00783908
https://hal.univ-antilles.fr/hal-00783908

Éditeur(s) : HAL CCSD Yokohama
Résumé : International audience
We introduce a convergent method for approximating a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a monotone equilibrium problem. Using the main convergence theorem we obtain results which improve, develop and unify several results in fixed point problems, variational inequalities and equilibrium problems.
Journal of Nonlinear and Convex Analysis

hal-00779989
https://hal.univ-antilles.fr/hal-00779989

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
BACKGROUND: An association between education and preterm delivery has been observed in populations across Europe, but differences in methodology limit comparability. We performed a direct cross-cohort comparison of educational disparities in preterm delivery based on individual-level birth cohort data. METHODS: The study included data from 12 European cohorts from Denmark, England, France, Lithuania, the Netherlands, Norway, Italy, Portugal, and Spain. The cohorts included between 2434 and 99 655 pregnancies. The association between maternal education and preterm delivery (22-36 completed weeks of gestation) was reported as risk ratios, risk differences, and slope indexes of inequality with 95% confidence intervals (CIs). RESULTS: Singleton preterm live delivery proportion varied between 3.7% and 7.5%. There were large variations between the cohorts in the distribution of education and maternal characteristics. Nevertheless, there were similar educational differences in risk of preterm delivery in 8 of the 12 cohorts with slope index of inequality varying between 2.2 [95% CI 1.1, 3.3] and 4.0 [95% CI 1.4, 6.6] excess preterm deliveries per 100 singleton deliveries among the educationally most disadvantaged, and risk ratio between the lowest and highest education category varying from 1.4 [95% CI 1.1, 1.8] to 1.9 [95% CI 1.2, 3.1]. No associations were found in the last four cohorts. CONCLUSIONS: Educational disparities in preterm delivery were found all over Europe. Despite differences in the distributions of education and preterm delivery, the results were remarkably similar across the cohorts. For those few cohorts that did not follow the pattern, study and country characteristics did not explain the differences.
ISSN: 0269-5022

hal-01146842
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01146842
DOI : 10.1111/ppe.12185
PUBMED : 25808200

Éditeur(s) : Université de la Rochelle
Résumé : In order to better understand the functioning of the Brouage intertidal mudflat (Marennes- Oléron Basin, France), its carbon-based trophic web has been modelled and analyzed. The foodweb building is based on the 4 step method of Inverse Analysis: 1) conceive an a priori model as the graph of compartments (nodes) between which exist fluxes of material (vertices). These vertices are the unknowns for the problem; 2) gather all the existing knowledge about the ecosystem and translate it into linear equations and inequalities involving the fluxes; 3) complete this set of data by common knowledge on the behaviour of the compartments and translate it into inequalities, 4) solve the obtained linear system under the parsimony principle to find a unique solution vector. The food-web analysis is based on. The first purpose of this work was a methodological one: inverse analysis method has been adapted to consider the seasonal and spatial variability of the temperate ecosystem: two seasons have been coupled in the computation and the area has been divided into three geographical zones along a cross-shore gradient. Hence, two types of physical exchanges are involved: the benthicpelagic ones and the advection ones. Statistical results can also be obtained by coupling Monte Carlo methods to Inverse Analysis. To study the obtained networks, new indices based on Markov Chains take delay into account in describing integrative transfers of material between compartments. This lets emerge the systems' properties that are not obvious at first sight and emphasizes the role of peculiar components. The second purpose was to apply such methods to the Brouage mudflat ecosystem in order to better understand its functioning. As the knowledge and methods evolve, various food webs were computed and analyzed with the help such indices and existing ones. Sensitivity analyses allow to point at the most crucial lacks of knowledge, which can orientate future field research. New data would improve the quality of the model in two ways: one the one hand, they would validate or invalidate the outcomes and on the other hand, they would give useful information to better constrain some of the black boxes and most uncertain fluxes, especially the advection and vertical flows. The main results of the study show a strongly seasonal system in which benthic and pelagic components are linked with intensity. The system is driven by its high local benthic primary production, but also depends on imports from the basin. Each of the 3 geographic zones has a peculiar functioning. The central zone corresponds to the classical description of European intertidal mudflats: very productive, it can feed the other regions. It is a production zone. The upper part is less productive but is fed by the middle one via the water column and can be exploited by shorebirds. It is a degradation zone (material is transformed for less qualitative). The lower part strongly depends on the basin imports for its functioning, as the cultivated bivalves act as a pump for pelagic material of which a great part is deposited under the cultivation structures (oyster racks or mussels "bouchots"). It is a transformation zone.
Un double objectif (méthodologique et appliqué) a été visé par une modélisation du réseau trophique de la vasière de Brouage (Bassin de Marennes Oléron, France) à l'aide de l'analyse inverse, et son étude à l'aide de l'analyse des réseaux. L'Analyse Inverse permet en effet de reconstruire l'ensemble du réseau à partir de données éparses, le problème du manque de données étant récurrent en Ecologie. Au plan méthodologique, l'analyse inverse a été adaptée à la prise en compte des caractères saisonnier et spatialement hétérogène d'un écosystème tempéré de zone intertidale : deux saisons ont ainsi été couplées et la vasière a été considérée le long d'un transect perpendiculaire au rivage et divisé en trois zones spatiales. Deux types de flux physiques interviennent donc : les flux verticaux de dépôt et remise en suspension, et les flux d'advection via la colonne d'eau. Des pistes d'amélioration et de nouvelles méthodes sont proposées. Un résultat sous forme statistique peut être obtenu en couplant l'utilisation de méthodes de Monte Carlo à l'analyse inverse pour la construction des réseaux trophiques. Les moyens d'étude des modèles ont été enrichis par la mise au point d'indices issus de la construction de chaînes de Markov et prenant en compte le caractère temporel des transferts de matière entre compartiments. Enfin, la transformation mathématique du modèle statique pour une étude dynamique de la stabilité de l'équilibre décrit est abordée. Plusieurs modèles ont été construits au cours de l'évolution des méthodes et de l'acquisition de connaissances sur le site. Des méthodes d'analyses existantes et d'autres mises au point dans le cadre de cet ouvrage ont été appliquées aux réseaux obtenus afin de faire émerger les propriétés du fonctionnement de la vasière et de souligner le rôle de certains compartiments. Des analyses de sensibilité permettent d'évaluer la robustesse des résultats et d'orienter les recherches futures en mettant en évidence les manques les plus cruciaux. Des données supplémentaires, notamment concernant les foraminifères benthiques, le zooplancton ou les mouvements verticaux du microphytobenthos permettront de fournir de meilleures contraintes et de valider (ou non) les résultats obtenus. Les principaux résultats montrent un système au fort caractère saisonnier dont les compartiments benthiques et pélagiques sont très liés. La production primaire benthique locale est un moteur important, mais qui ne suffirait pas à suppléer l'indispensable importation de matériel détritique. Le découpage de la vasière en trois zones fait apparaître les particularités de chacune. La zone centrale correspond à la description classique des « vasières intertidales européennes » : très productive, elle peut alimenter les autres régions. C'est une zone de production et d'exportation. La partie supérieure est moins productive et reçoit de la matière de la zone de milieu d'estran via la colonne d'eau. Sa production secondaire peut alors être exploitée par les limicoles, nombreux en hiver. C'est une zone de dégradation et d'exportation. Le bas d'estran dépend fortement des importations extérieures, « pompées » par les bivalves cultivés qui sont ainsi directement responsables d'une forte sédimentation sous les structures mytilicoles et ostréicoles. C'est une zone de transformation.

Droits : info:eu-repo/semantics/openAccess
http://archimer.ifremer.fr/doc/2005/these-2260.pdf
http://archimer.ifremer.fr/doc/00000/2260/

Éditeur(s) : HAL CCSD
Résumé : International audience
It is established that the multivalued quasi variational inequalities in uniformly smooth Banach spaces are equivalent to the fixed-point problem. We use this equivalence to suggest and analyze some iterative algorithms for quasi variational inequalities with noncompact sets in Banach spaces. Our results are new and represent a significant improvement of the previously known results.;
JIPAM

hal-00778168
https://hal.univ-antilles.fr/hal-00778168

Éditeur(s) : HAL CCSD
Résumé : International audience
The paper deals with iterative schemes for finding a zero of a maximal monotone operator. A combination of the auxiliary principle with the Tikhonov method is considered. Under some assumptions the sequence generated by such an iterative scheme is shown to converge to a solution of the problem that is required to satisfy an associated variational inequality
Lecture notes in economics and mathematical systems

hal-00773198
https://hal.univ-antilles.fr/hal-00773198

Éditeur(s) : HAL CCSD American Mathematical Society
Résumé : International audience
We define an abstract notion of subdifferential operator and an associated notion of smoothness of a norm covering all the standard situations. In particular, a norm is smooth for the Gâteaux (Fréchet, Hadamard, Lipschitz-smooth) subdifferential if it is Gâteaux (Fréchet, Hadamard, Lipschitz) smooth in the classical sense, while on the other hand any norm is smooth for the Clarke-Rockafellar subdifferential. We then show that lower semicontinuous functions on a Banach space satisfy an Approximate Mean Value Inequality with respect to any subdifferential for which the norm is smooth, thus providing a new insight on the connection between the smoothness of norms and the subdifferentiability properties of functions. The proof relies on an adaptation of the ''smooth'' variational principle of Borwein-Preiss. Along the same vein, we derive subdifferential criteria for coercivity, Lipschitz behavior, cone-monotonicity, quasiconvexity, and convexity of lower semicontinuous functions which clarify, unify and extend many existing results for specific subdifferentials.
ISSN: 0002-9947

hal-00699220
https://hal.archives-ouvertes.fr/hal-00699220

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
In this paper, using the penalty method in conjunction with graph-convergence, we study the existence of solutions for a class of generalized variational inequalities with variational problem constraints. Our results extend, improve and develop some known results in this field. Our method of proofs is very simple and does not use the hemicontinuity nor the pseudo-continuity properties of monotone operators.
ISSN: 1862-4472

hal-00776643
https://hal.univ-antilles.fr/hal-00776643
DOI : 10.1007/s11590-010-0271-1

Éditeur(s) : HAL CCSD
Résumé : International audience
To solve general variational inequalities considered in Robinson [9], we propose a generalized version of an algorithm introduced by Bermudez and Moreno [3]. Our results extend, improve and develop some known results in this field.
Advanced Modeling and Optimization

hal-00783892
https://hal.univ-antilles.fr/hal-00783892

Éditeur(s) : HAL CCSD
Résumé : International audience
An iterative method for solving set-valued variational inequalities is considered and its convergence properties are studied under strong monotonicity and coercivity conditions. The results obtained in this paper include, as a special case, some known results in this field.
Mathematical Inequalities & Applications

hal-00776616
https://hal.univ-antilles.fr/hal-00776616

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Several studies have documented that more deprived populations tend to live in areas characterized by higher levels of environmental pollution. Yet, time trends and geographic patterns of this disproportionate distribution of environmental burden remain poorly assessed, especially in Europe. We investigated the spatial and temporal relationship between ambient air nitrogen dioxide (NO2) concentrations and socioeconomic and demographic data in four French metropolitan areas (Lille in the North, Lyon in the center, Marseille in the South, and Paris) during two different time periods. The geographical unit used was the census block. The dependent variable was the NO2 annual average concentration (μg/m(3)) per census block, and the explanatory variables were a neighborhood deprivation index and socioeconomic and demographic data derived from the national census. Generalized additive models were used to account for spatial autocorrelation. We found that the strength and direction of the association between deprivation and NO2 estimates varied between cities. In Paris, census blocks with the higher social categories are exposed to higher mean concentrations of NO2. However, in Lille and Marseille, the most deprived census blocks are the most exposed to NO2. In Lyon, the census blocks in the middle social categories were more likely to have higher concentrations than in the lower social categories. Despite a general reduction in NO2 concentrations over the study period in the four metropolitan areas, we found contrasting results in the temporal trend of environmental inequalities. There is clear evidence of city-specific spatial and temporal environmental inequalities that relate to the historical socioeconomic make-up of the cities and its evolution. Hence, general statements about environmental and social inequalities can be made.
ISSN: 0013-9351

hal-01063900
https://hal.archives-ouvertes.fr/hal-01063900
DOI : 10.1016/j.envres.2014.07.017
PUBMED : 25199972

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Mapping spatial distributions of disease occurrence can serve as a useful tool for identifying exposures of public health concern. Infant mortality is an important indicator of the health status of a population. Recent literature suggests that neighborhood deprivation status can modify the effect of air pollution on preterm delivery, a known risk factor for infant mortality. We investigated the effect of neighborhood social deprivation on the association between exposure to ambient air NO2 and infant mortality in the Lille and Lyon metropolitan areas, north and center of France, respectively, between 2002 and 2009. We conducted an ecological study using a neighborhood deprivation index estimated at the French census block from the 2006 census data. Infant mortality data were collected from local councils and geocoded using the address of residence. We generated maps using generalized additive models, smoothing on longitude and latitude while adjusting for covariates. We used permutation tests to examine the overall importance of location in the model and identify areas of increased and decreased risk. The average death rate was 4.2‰ and 4.6‰ live births for the Lille and Lyon metropolitan areas during the period. We found evidence of statistically significant precise clusters of elevated infant mortality for Lille and an east-west gradient of infant mortality risk for Lyon. Exposure to NO2 did not explain the spatial relationship. The Lille MA, socioeconomic deprivation index explained the spatial variation observed. These techniques provide evidence of clusters of significantly elevated infant mortality risk in relation with the neighborhood socioeconomic status. This method could be used for public policy management to determine priority areas for interventions. Moreover, taking into account the relationship between social and environmental exposure may help identify areas with cumulative inequalities.
ISSN: 0048-9697

inserm-00838330
http://www.hal.inserm.fr/inserm-00838330
DOI : 10.1016/j.scitotenv.2013.03.027
PUBMED : 23563257

Éditeur(s) : HAL CCSD Society for Industrial and Applied Mathematics
Résumé : International audience
We establish a general Fermat rule for the problem of minimizing a lower semicontinuous function on a convex subset of a Banach space. Our basic tool is a constrained variational principle derived from the "smooth" variational principle of Borwein and Preiss. Specializing the Fermat rule to the case when the convex set is a "drop," we obtain a multidirectional Rolle-type inequality from which, in turn, we deduce a multidirectional mean value inequality, in the line of Clarke and Ledyaev. We follow the abstract approach of our previous paper [Trans. Amer. Math. Soc., 347 (1995), pp. 4147-4161], thus covering all standard situations met in applications, while stressing the links between the results and the few key properties that are needed.
ISSN: 1052-6234

hal-00699204
https://hal.archives-ouvertes.fr/hal-00699204

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
In France, reducing social health inequalities has become an explicit goal of health policies over the past few years, one of its objectives is specifically the reduction of the perinatal mortality rate. This study investigates the association between infant mortality and social deprivation categories at a small area level in the Lille metropolitan area, in the north of France, to identify census blocks where public authorities should prioritize appropriate preventive actions. We used census data to establish a neighbourhood deprivation index whose multiple dimensions encompass socioeconomic characteristics. Infant mortality data were obtained from the Lille metropolitan area municipalities to estimate a death rate at the census tract level. We used Bayesian hierarchical models in order to reduce the extra variability when computing relative risks (RR) and to assess the associations between infant mortality and deprivation. Between 2000 and 2009, 668 cases of infant death occurred in the Lille metropolitan area (4.2 per 1,000 live births). The socioeconomic status is associated with infant mortality, with a clear gradient of risk from the most privileged census blocks to the most deprived ones (RR = 2.62, 95 % confidence interval [1.87; 3.70]). The latter have 24.6 % of families who were single parents and 29.9 % of unemployed people in the labor force versus 8.5 % and 7.7 % in the former. Our study reveals socio-spatial disparities in infant mortality in the Lille metropolitan area and highlights the census blocks most affected by the inequalities. Fine spatial analysis may help inform the design of preventive policies tailored to the characteristics of the local communities.
ISSN: 1092-7875

hal-00876255
https://hal.archives-ouvertes.fr/hal-00876255
DOI : 10.1007/s10995-013-1251-8
PUBMED : 23479336

Éditeur(s) : HAL CCSD North Atlantic Science Publishing Company
Résumé : International audience
In this paper, we extend the sensitivity analysis framework developed recently for variational inequalities by Noor and Yen to variational inclusions relying on Wiener-Hopf equation techniques. We prove the continuity and the Lipschitz continuity of the locally unique solution to parametric variational inclusions without assuming differentiability of the given data.
ISSN: 1048-9533

hal-00779240
https://hal.univ-antilles.fr/hal-00779240
https://hal.univ-antilles.fr/hal-00779240/document
https://hal.univ-antilles.fr/hal-00779240/file/681979_4_.pdf

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : 4 pages
International audience
We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point. This provides a characterization of the monotone polar of subdifferentials of lower semicontinuous functions: it is a common subset of their graphs which depends only on the function.
ISSN: 1862-4472

hal-00842670
https://hal.archives-ouvertes.fr/hal-00842670
ARXIV : 1307.1826
DOI : 10.1007/s11590-013-0693-7

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems
ISSN: 0163-0563

hal-00776641
https://hal.univ-antilles.fr/hal-00776641
DOI : 10.1080/01630563.2011.619676

Éditeur(s) : HAL CCSD SpringerOpen
Résumé : International audience
We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality,, where denotes the normal cone to the set of fixed point of the original nonexpansive mapping and a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.
ISSN: 1687-1820

hal-00780237
https://hal.univ-antilles.fr/hal-00780237
https://hal.univ-antilles.fr/hal-00780237/document
https://hal.univ-antilles.fr/hal-00780237/file/1687-1812-2006-95453.pdf
DOI : 10.1155/FPTA/2006/95453

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The main purpose of this paper is to propose a deterministic mathematical model with control variable which describes the spatiotemporal spread of emph{Salmonella} within a laying flock. This model assume an indirect transmission of the disease within the flock through the bacteria density in the environment. We provide a mathematical analyze of the null controllability of the model: we begin to construct a family of solutions to the linear null-controllability problem using the the Carleman inequality. Then, by a generalized Leray-Shauder fixed point theorem, we show that one can bring the system to rest at final time T.
ISSN: 0307-904X

Droits : info:eu-repo/semantics/OpenAccess
hal-01683267
https://hal.univ-antilles.fr/hal-01683267
https://hal.univ-antilles.fr/hal-01683267/document
https://hal.univ-antilles.fr/hal-01683267/file/APM-S-13-02490-1.pdf