Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A set-valued upper semi-continuous map is called an Rδ -map if each of its values is an Rδ -set (we recall that an Rδ -set is a space that can be represented as the intersection of a decreasing sequence of compact AR-spaces). We prove that a compact set-valued map of an AR-space into itself has a fixed point provided it can be factorized by an arbitrary finite number of Rδ -maps through ANR-spaces. This fact is a consequence of a more general result which is the main goal of this note. The proof relies on a refinement of the approximation technique and does not make use of homological tools.
ISSN: 0166-8641

hal-00699222
https://hal.archives-ouvertes.fr/hal-00699222

Éditeur(s) : HAL CCSD MDPI
Résumé : International audience
Malaria remains one of the most common vector-borne diseases in the world and the definition of novel control strategies can benefit from the modeling of transmission processes. However, data-driven models are often difficult to build, as data are very often incomplete, heterogeneous in nature and in quality, and/or biased. In this context, a knowledge-based approach is proposed to build a robust and general landscape-based hazard index for malaria transmission that is tailored to the Amazonian region. A partial knowledge-based model of the risk of malaria transmission in the Amazonian region, based on landscape features and extracted from a systematic literature review, was used. Spatialization of the model was obtained by generating land use and land cover maps of the cross-border area between French Guiana and Brazil, followed by computing and combining landscape metrics to build a set of normalized landscape-based hazard indices. An empirical selection of the best index was performed by comparing the indices in terms of adequacy with the knowledge-based model, intelligibility and correlation with P. falciparum incidence rates. The selected index is easy to interpret and successfully represents the current knowledge about the role played by landscape patterns in malaria transmission within the study area. It was significantly associated with P. falciparum incidence rates, using the Pearson and Spearman correlation coefficients (up to 0.79 and 0.75, respectively; p-value < 0.001), and the linear regression coefficient of determination (reaching 0.63; p-values < 0.001). This study establishes a spatial knowledge-driven, landscape-based hazard malaria index using remote sensing that can be easily produced on a regular basis and might be useful for malaria prediction, surveillance, and control. Keywords: remote sensing; land use and land cover; landscape metric; knowledge-based hazard modeling; malaria; cross-border area between French Guiana and Brazil
ISSN: 2072-4292

hal-01355255
https://hal.archives-ouvertes.fr/hal-01355255
https://hal.archives-ouvertes.fr/hal-01355255/document
https://hal.archives-ouvertes.fr/hal-01355255/file/010066865.pdf
IRD : fdi:010066865

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with variational inclusions of the form 0 2 f(x) + g(x) K where f is smooth function from a re exive Banach space X into a Banach space Y , g is a Lipschitz function from X into Y and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by an extension of the Zincenko's method which can be seen as a perturbed Newton's method. Numerical results are given at the end of the paper.
Revista Investigacion Operacional

hal-00924143
https://hal.archives-ouvertes.fr/hal-00924143

Éditeur(s) : HAL CCSD Springer
Résumé : International audience
In this chapter, the aim is the solving of variational inclusions fo the form 0_in f(x)+F(x), where f is a subanalytic and locally Lipschitz function, F is a set-valued map with closed graph. The methods are developped using the metric regularity of (f+F) or the Aubin property of (f+F)^{-1}, and often lead to a superlinear convergence.
Handbook of optimization, from classical to modern approach

ISBN : 978-3-642-30503-0
hal-00757674
https://hal.archives-ouvertes.fr/hal-00757674
DOI : 10.1007/978-3-642-30504-7-38

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
An approximation method which combines Tikhonov method with the proximal point algorithm, is presented. Conditions which guarantee the convergence to a particular element of the solution set, are provided. A particular attention is given to the convex and convex-concave optimization cases.
ISSN: 0233-1934

hal-00815513
https://hal.univ-antilles.fr/hal-00815513
DOI : 10.1080/02331939608844217

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Taking advantage of recent developments in the theory of generalized differentiation, we present an inverse mapping theorem for set-valued maps and prove its stability under small linear perturbations. Using variational convergences of set-valued mappings, we present as well an approximate version of our inverse theorem.
Journal of Mathematical Analysis and applications

hal-01023227
https://hal.archives-ouvertes.fr/hal-01023227
DOI : 10.1016/j.jmaa.2014.07.006

Résumé : Dans cette thèse, nous nous intéressons à des inclusions de la forme 0∈ f( x) + F(x), où f est une application univoque et F est une application multivoque à graphe fermé. Ces dernières années, diverses méthodes de résolutions d'inclusions de ce type ont été développées par les chercheurs et, après un bref rappel sur quelques notions d'analyse (univoque et multivoque) nous en présentons quelques unes utilisant l'hypothèse de régularité métrique sur l'application multivoque. Dans la suite de notre travail, plutôt que d'utiliser cette hypothèse de régularité métrique, nous lui préférons des hypothèses directement liées à la solution qui sont la semistabilité et l'hemistabilité. Notons que la semistabilité d'une solution x̅ de l'inclusion 0∈G(x) est en fait équivalente à la sous-régularité métrique forte de l'application multivoque G en x̅ pour 0. Après avoir présenté des méthodes utilisant la semistabilité et l'hemistabilité, nous exposons les nouveaux résultats auxquels nous avons abouti qui consistent essentiellement en des améliorations des méthodes présentées. Ce que nous entendons par améliorations se décline en deux points principaux : soit nous obtenons un meilleur taux de convergence, soit nous utilisons des hypothèses plus faibles qui nous permettent d'obtenir des taux de convergence similaires.
In this thesis, we focus on inclusions in the form of 0∈ f( x) + F(x), where f is a single-valued function and F is a set-valued map with closed graph. In the last few years, various methods to solve such inclusions have been developed; after having recalled some notions in analysis (single-valued and set-valued) we present some of them using metric regularity on the set-valued map. Then, instead of considering this metric regularity assumption, we prefer assumptions which are directly connected to the solution, that are semistability and hemistability. One can note that semistabily of a solution x̅ of the inclusion 0∈G(x) is actually equivalent strong metric subregularity on the set-valued map G at x̅ for 0. After having presented some methods using semistability and hemistability, we show the new results we obtained, most of them being improvement of the presented methods. What we mean by improvement is mainly a better convergence rate on the one hand, and weaker assumptions that lead to similar convergence rate, on the other.

http://www.theses.fr/2012AGUY0594/document

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
The aim of this study is the approximation of a solution x* of a ganeralized equation 0 in f(x)+F(x) in Banach spaces, where f is a single-valued function whose second order Frechet derivative satisfies an Hölder condition and F stands for a set-valed map with closed graph. Using a fixed point theorem and the Aubin property of F, we show the existence and the superquadratic convergence of a sequence derived from a midpoint method.
ISSN: 0167-8019

hal-00642118
https://hal.archives-ouvertes.fr/hal-00642118

Éditeur(s) : HAL CCSD Yokohama
Résumé : International audience
We make use of the viscosity technique to develop a convergent method for approximating a common element of the set of fixed points of a demicontractive operator and the set of solutions of a monotone equilibrium problem. The proposed algorithm is obtained by coupling a modified hybrid steepest descent method with the extragradient algorithm. Under mild conditions, the strong convergence of the sequences generated by the algorithm is obtained. Using this result we obtain two corollaries which improve or develop several corresponding results in this field.
Journal of Nonlinear and Convex Analysis

hal-00779988
https://hal.univ-antilles.fr/hal-00779988

Éditeur(s) : HAL CCSD Tsing Hua University
Résumé : International audience
This paper deals with variational inclusions of the form : $0in varphi(z)+F(z)$ where $varphi$ is a single-valued function admitting a second order Fréchet derivative and $F$ is a set-valued map from $R^q$ to the closed subsets of $R^q$. In order to approximate a solution $bar z$ of the previous inclusion, we use an iterative scheme based on a multipoint method. We obtain, thanks to some semistability properties of $bar z$, local superquadratic or cubic convergent sequences
ISSN: 1607-2510

hal-00728816
https://hal.archives-ouvertes.fr/hal-00728816

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We investigate the existence of several kinds of prederivatives for set-valued mappings enjoying convex properties. Then, we established both necessary and sufficient optimality conditions, involving such prederivatives, for set optimization problems.
ISSN: 0925-5001

hal-01172386
https://hal.archives-ouvertes.fr/hal-01172386
DOI : 10.1007/s10898-015-0338-8

Éditeur(s) : HAL CCSD
Résumé : International audience
We deal with a perturbed version of a Hummel-Seebeck type method to approximate a solution of variational inclusions of the form : 0 ∈ Φ(z) + F(z) where Φ is a single-valued function twice continuously Fréchet differentiable and F is a set-valued map from Rn to the closed subsets of Rn. This framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods (see [1]). We obtain, thanks to some semistability and another property (which is close to the hemistability) of the solution z ̄ of the previous inclusion, the local existence of a sequence that is superquadratically or cubically convergent.
ISSN: 2518-3680

hal-01630560
https://hal.archives-ouvertes.fr/hal-01630560
DOI : 10.22606

Résumé : Dans cette thèse nous présentons dans un premier temps une nouvelle notion de différentiabilité généralisée pour les applications multivoques, faisant intervenir des applications positivement homogènes: la H-différentiabilité. Nous étudions la stabilité de cette notion en utilisant la convergence de Fischer, d'abord dédiée aux ensembles mais que nous avons adaptée aux applications multivoques. Nous nous intéressons ensuite à l'étude de la dépendance continue des ensembles de points fixes d'une application multivoque contractante par rapport aux données. Finalement nous analysons la convergence d'une méthode d'approximations successives de type forward-backward splitting, des zéros de la somme de deux opérateurs multivoques non monotones, jouissants notamment de propriétés de pseudo H-différentiabilité
In this thesis we present at first a new concept of generalized differentiation for setvalued mappings, involving positively homogeneous applications: the H-differentiability. We study the stability of this notion by using Fischer convergence,firstly dedicated to sets but which we have adapted to set-valued mappings. We establish the continuous dependence of fixed points sets of set-valued contraction and finally we study the convergence of a forward-backward splitting method for approximating the zeros of the sum of two non-monotone set-valued mappings, notably using properties of pseudo H-differentiability.

http://www.theses.fr/2011AGUY0490/document

Éditeur(s) : HAL CCSD American Mathematical Society
Résumé : International audience
We propose to study fragmentability of set-valued mappings not only for a given single mapping, but also for a sequence of mappings associated with the initial one. It turns out that this property underlies several variational principles, such as for example the Deville-Godefroy-Zizler variational principle and the Stegall variational principle, by providing a common path for proof.
ISSN: 0002-9939

hal-00698981
https://hal.archives-ouvertes.fr/hal-00698981

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper.
Serdica Math. J.

hal-00924150
https://hal.archives-ouvertes.fr/hal-00924150

Résumé : Les méthodes classiques d'analyse d'images satellites sont inadaptées au volume actuel du flux de données. L'automatisation de l'interprétation de ces images devient donc cruciale pour l'analyse et la gestion des phénomènes observables par satellite et évoluant dans le temps et l'espace. Ce travail vise à automatiser la cartographie dynamique de l'occupation du sol à partir d'images satellites, par des mécanismes expressifs, facilement interprétables en prenant en compte les aspects structurels de l'information géographique. Il s'inscrit dans le cadre de l'analyse d'images basée objet. Ainsi, un paramétrage supervisé d'un algorithme de segmentation d'images est proposé. Dans un deuxième temps, une méthode de classification supervisée d'objets géographiques est présentée combinant apprentissage automatique par programmation logique inductive et classement par l'approche multi-class rule set intersection. Ces approches sont appliquées à la cartographie de la bande côtière Guyanaise. Les résultats démontrent la faisabilité du paramétrage de la segmentation, mais également sa variabilité en fonction des classes de la carte de référence et des données d'entrée. Les résultats de la classification supervisée montrent qu'il est possible d'induire des règles de classification expressives, véhiculant des informations cohérentes et structurelles dans un contexte applicatif donnée et conduisant à des valeurs satisfaisantes de précision et de KAPPA (respectivement 84,6% et 0,7). Ce travail de thèse contribue ainsi à l'automatisation de la cartographie dynamique à partir d'images de télédétection et propose des perspectives originales et prometteuses.
Classical methods for satellite image analysis are inadequate for the current bulky data flow. Thus, automate the interpretation of such images becomes crucial for the analysis and management of phenomena changing in time and space, observable by satellite. Thus, this work aims at automating land cover cartography from satellite images, by expressive and easily interpretable mechanism, and by explicitly taking into account structural aspects of geographic information. It is part of the object-based image analysis framework, and assumes that it is possible to extract useful contextual knowledge from maps. Thus, a supervised parameterization methods of a segmentation algorithm is proposed. Secondly, a supervised classification of geographical objects is presented. It combines machine learning by inductive logic programming and the multi-class rule set intersection approach. These approaches are applied to the French Guiana coastline cartography. The results demonstrate the feasibility of the segmentation parameterization, but also its variability as a function of the reference map classes and of the input data. Yet, methodological developments allow to consider an operational implementation of such an approach. The results of the object supervised classification show that it is possible to induce expressive classification rules that convey consistent and structural information in a given application context and lead to reliable predictions, with overall accuracy and Kappa values equal to, respectively, 84,6% and 0,7. In conclusion, this work contributes to the automation of the dynamic cartography from remotely sensed images and proposes original and promising perpectives

http://www.theses.fr/2013AGUY0671/document

Éditeur(s) : HAL CCSD
Résumé : International audience
Geographic Information Systems (GIS) help addressing geographical and environmental issues by providing information about a region or a city as a set of maps (layers), each one displaying information about a given theme like roads, vegetation, tourist spots or museums for instance. By combining different layers on a region, one can associate a given area to characteristics from their related themes. Indeed, the information from two or more layers might be merged and then transformed into a new layer as defined in map "algebra". When a theme vocabulary is organized as a taxonomy with concepts linked by is-a relationships, there are different ways to annotate an area with a concept depending on the level selected into the layer taxonomy. In this paper, we present an heuristic- based approach for an optimal merging of such layers in a GIS. Our goal is to generate new layers which sum up information from several themes in a most useful way. Two optimization criteria are considered, the average size of resulting areas and the average informative value of their resulting annotation. We demonstrate the validity of the proposed solution, firstly, on a formal example, and then, on a real world application.
Proceedings of the 4th International Conference on Advanced Geographic Information Systems, Applications, and Services
Valencia, Spain

hal-00679555
https://hal.archives-ouvertes.fr/hal-00679555

Éditeur(s) : HAL CCSD
Résumé :  
Improvement of wood quality related traits is currently hampered by costly chemical and technological assays and the necessity to wait until the trees are nearly mature to evaluate wood properties. The availability of a vast quantity of genomic data opens now a new avenue to identify early selection criteria based on molecular information and therefore increase selection efficiency. Association mapping is becoming a method of choice to identify QTN (quantitative trait nucleotide) that contribute to complex trait variation. The implementation of this approach requires on the one hand knowledge of the molecular mechanisms underlying trait variation and polymorphism within candidate genes, and on the other hand the availability of phenotypically well characterized genetic material. We are developing this strategy in the frame of the French maritime pine breeding program, an economically important forest tree species in the South Western Europe. About 500 trees from the breeding population were evaluated for wood physical and chemical properties through the analysis of 2,800 half-sib progenies and 1,500 clones in 8 field tests. These same trees are being genotyped at 185 SNPs obtained from the sequencing of 41 candidate genes, and an additional set of 200 eSNPs detected in 147 EST-contigs (to be used as control). Statistical association between the breeding values of the 500 trees and their respective genotypes will be tested using mixed models accounting for relatedness among individuals of the breeding population.
IUFRO-CTIA joint conference, "Adaptation, Breeding and Conservation in the Era of Forest Tree Genomics and Environmental Change"
Québec City, Canada

hal-01032075
https://hal.archives-ouvertes.fr/hal-01032075

Éditeur(s) : HAL CCSD
Résumé : The midpoint method was previously used in the solving of equations and in this work, the aim is to adapt the theory to the set-valued analysis in order to approach solutions of generalized equations of the form 0_inf(x)+F(x). In particular, we show the existence and convergence fo sequences provided the second order derivative of the function f satisfies a Hölder condition, or a center-Hölder condition.
GDR MOA
Sainte-Anne, Guadeloupe

hal-00757686
https://hal.archives-ouvertes.fr/hal-00757686