Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the function is convex.
ISSN: 0925-5001

hal-00761658
https://hal.archives-ouvertes.fr/hal-00761658
ARXIV : 1212.0532
DOI : 10.1007/s10898-013-0078-6

Éditeur(s) : Paris : Dusacq

Provenance : Archives départementales de Guadeloupe
Permalien : http://www.manioc.org/patrimon/ADG18219
ADG18219

Éditeur(s) : HAL CCSD
Résumé : International audience
We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak∗ Lipschitz Separation property, a strong Compact Separation property and a Minimal property for the analytic approximate subdifferential of Ioffe.
Serdica. Mathematical Journal

hal-00694603
https://hal.archives-ouvertes.fr/hal-00694603

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

Résumé : Seconde édition
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Fondation Clément
Permalien : http://www.manioc.org/patrimon/FCL18027
FCL18027

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A multifunction Γ is called a Kakutani multifunction if there exist two nonempty convex sets X and Y , each in a Hausdorff topological vector space, such that Γ : X → Y is upper semi-continuous with nonempty compact convex values. We prove the following extension of the Kakutani fixed point theorem : Let Γ : X → X be a multi-function from a simplex X into itself ; if Γ can be factorized by an arbitrary finite number of Kakutani multifunctions, then Γ has a fixed point. The proof relies on a simplicial approximation technique and the Brouwer fixed point theorem. Extensions to infinite-dimensional spaces and applications to game theory are given.
Journal of Mathematical Analysis and applications

hal-00699225
https://hal.archives-ouvertes.fr/hal-00699225

Éditeur(s) : Ministère de la marine et des colonies
Résumé : Description des plantes des colonies françaises.
Siècle(s) traité(s) : 18
Droits : Domaine public
Provenance : Fondation Clément
Permalien : http://www.manioc.org/patrimon/FCL18019
FCL18019

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fréchet differentiability of convex continuous functions on Y (Asplund property), generic existence of linear perturbations for lower semicontinuous functions on X to have a strong minimum (Stegall variational principle), and dentability of bounded subsets of X (Radon-Nikodým Property).
ISSN: 0927-6947

hal-00694604
https://hal.archives-ouvertes.fr/hal-00694604

Éditeur(s) : Paris : Librairie Larousse
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Communauté d'agglomération de La Rochelle. Médiathèque Michel-Crépeau
Permalien : http://www.manioc.org/patrimon/MMC16023-2
MMC16023-2

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The growth of relief in active tectonic areas is mainly controlled by the interactions between tectonics and surface processes (erosion and sedimentation). The study of long-lived morphologic markers formed by these interactions can help in quantifying the competing effects of tectonics, erosion and sedimentation. In regions experiencing active extension, river-long profiles and faceted spurs (triangular facets) can help in un- derstanding the development of mountainous topography along normal fault scarps. In this study, we devel- oped analogue experiments that simulate the morphologic evolution of a mountain range bounded by a normal fault. This paper focuses on the effect of the fault slip rate on the morphologic evolution of the foot- wall by performing three analogue experiments with different fault slip rates under a constant rainfall rate. A morphometric analysis of the modelled catchments allows comparing with a natural case (Tunka half- graben, Siberia). After a certain amount of fault slip, the modelled footwall topographies of our models reaches a dynamic equilibrium (i.e., erosion balances tectonic uplift relative to the base level) close to the fault, whereas the topography farther from the fault is still being dissected due to regressive erosion. We show that the rates of vertical erosion in the area where dynamic equilibrium is reached and the rate of re- gressive erosion are linearly correlated with the fault throw rate. Facet morphology seems to depend on the fault slip rate except for the fastest experiment where faceted spurs are degraded due to mass wasting. A stream-power law is computed for the area wherein rivers reach a topographic equilibrium. We show that the erosional capacity of the system depends on the fault slip rate. Finally, our results demonstrate the pos- sibility of preserving convex river-long profiles on the long-term under steady external (tectonic uplift and rainfall) conditions.
ISSN: 0040-1951

hal-00646966
https://hal.archives-ouvertes.fr/hal-00646966
https://hal.archives-ouvertes.fr/hal-00646966/document
https://hal.archives-ouvertes.fr/hal-00646966/file/preprint_Strak_2011.pdf
DOI : 10.1016/j.tecto.2011.10.005

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We consider a variable Krasnosel'skii-Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping proxλf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula xk+1=(1−αk)xk+αkproxλkfxk, where (αk) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition.
ISSN: 0362-546X

hal-00778175
https://hal.univ-antilles.fr/hal-00778175
DOI : 10.1016/j.na.2009.07.011

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Starting from a locally convex metrisable topological space and from any asymptotic scale, we construct a generalized extension of this space. To those extensions, we associate Hausdorff topologies. We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces. We show that such mappings extend in a canonical way to mappings between the respective generalized extensions. We give an application to nonlinear Dirichlet boundary value problems with singular data in the framework of generalized extensions
ISSN: 0026-9255

hal-01529549
https://hal.univ-antilles.fr/hal-01529549

Éditeur(s) : HAL CCSD EDP Sciences
Résumé : International audience
In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order damped evolution equations, which are governed by the sum of the gradient operator of a convex differentiable potential function , and a maximal monotone operator which is assumed to be cocoercive. Under a sharp condition involving the viscous and the cocoercive parameters, it is proved that each trajectory weakly converges to an equilibrium. Passing from weak to strong convergence is obtained by introducing an asymptotically vanishing Tikhonov-like regularizing term. As special cases, we recover the asymptotic analysis of the heavy ball with friction dynamic attached to a convex potential, the second-order gradient-projection dynamic, and the second-order dynamic governed by the Yosida approximation of a general maximal monotone operator. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of constrained optimization, dynamical approach to Nash equilibria for noncooperative games, and asymptotic stabilization in the case of a continuum of equilibria.
ISSN: 1292-8119

hal-00803774
https://hal.archives-ouvertes.fr/hal-00803774
https://hal.archives-ouvertes.fr/hal-00803774/document
https://hal.archives-ouvertes.fr/hal-00803774/file/ATTOUCH-MAINGE-09-04-2010-COCV.pdf
DOI : 10.1051/cocv/2010024

Éditeur(s) : Paris : A. Challamel
Siècle(s) traité(s) : 20
Droits : Domaine public
Provenance : Collectivité territoriale de Guyane. Bibliothèque Alexandre-Franconie
Permalien : http://www.manioc.org/patrimon/FRA11113
FRA11113

Éditeur(s) : Monachii ; Lipsiae : apud R. Oldenbourg in comm.
Extrait de : Flora brasiliensis : enumeratio plantarum in Brasilia hactenus detectarum quas suis aliorumque botanicorum studiis descriptas et methodo naturali digestas partim icone illustratas
Résumé : Édition : 1874-1900
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Université Toulouse III - Paul Sabatier. Service Commun de la Documentation
Permalien : http://www.manioc.org/patrimon/TLS17088
TLS17088

Éditeur(s) : Monachii ; Lipsiae : apud Frid. Fleischer in comm.
Extrait de : Flora brasiliensis : enumeratio plantarum in Brasilia hactenus detectarum quas suis aliorumque botanicorum studiis descriptas et methodo naturali digestas partim icone illustratas
Résumé : Édition : 1893-1896
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Université Toulouse III - Paul Sabatier. Service Commun de la Documentation
Permalien : http://www.manioc.org/patrimon/TLS17063
TLS17063

Éditeur(s) : HAL CCSD
Résumé : International audience
We start from a basic version of the Hahn-Banach theorem, of which we provide a proof based on Tychonoff's theorem on the product of compact intervals. Then, in the first section, we establish conditions ensuring the existence of affine functions lying between a convex function and a concave one in the setting of vector spaces -- this directly leads to the theorems of Hahn-Banach, Mazur-Orlicz and Fenchel. In the second section, we caracterize those topological vector spaces for which certain convex functions are continuous -- this is connected to the uniform boundedness theorem of Banach-Steinhaus and to the closed graph and open mapping theorems of Banach. Combining both types of results readily yields topological versions of the theorems of the first section.
Nonconvex Optim. Appl.
Erice, Italy

Droits : info:eu-repo/semantics/OpenAccess
hal-00699215
https://hal.archives-ouvertes.fr/hal-00699215
https://hal.archives-ouvertes.fr/hal-00699215/document
https://hal.archives-ouvertes.fr/hal-00699215/file/M_NonconvexOptimAppl98.pdf

Éditeur(s) : Lipsiae : apud Frid. Fleischer in comm.
Extrait de : Flora brasiliensis : enumeratio plantarum in Brasilia hactenus detectarum quas suis aliorumque botanicorum studiis descriptas et methodo naturali digestas partim icone illustratas
Résumé : Edition : 1870-1876
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Université Toulouse III - Paul Sabatier. Service Commun de la Documentation
Permalien : http://www.manioc.org/patrimon/TLS17094
TLS17094

Éditeur(s) : HAL CCSD
Résumé : International audience
J. Convex Anal.

hal-00756785
https://hal.archives-ouvertes.fr/hal-00756785

Éditeur(s) : Paris : Challamel
Siècle(s) traité(s) : 19
Droits : Domaine public
Provenance : Collectivité territoriale de Martinique. Bibliothèque Schoelcher
Permalien : http://www.manioc.org/patrimon/SCH13267
SCH13267