Éditeur(s) : HAL CCSD
Résumé : International audience
The main purpose of this note is to propose viscosity approximation methods which amount to selecting a particular fixed-point of a given nonexpansive self mapping in a general Hilbert space. The connection with the selection principles of Attouch, in the context of convex minimization and monotone inclusion problems, is made and an application to a semi-coercive elliptic problem is then stated. Key words: nonexpansive mappings, fixed-points, monotone operators, iterative methods, convex optimization, selection, penalty ...
Lecture notes in economics and mathematical systems

hal-00776623
https://hal.univ-antilles.fr/hal-00776623

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 Elsevier
Résumé : International audience
ISSN: 0377-0427

hal-00530820
https://hal.archives-ouvertes.fr/hal-00530820
DOI : 10.1016/j.cam.2008.08.014

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed-point of a given nonexpansive self-mapping.
Journal of Mathematical Analysis and applications

hal-00776600
https://hal.univ-antilles.fr/hal-00776600
DOI : 10.1006/jmaa.1999.6615

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : Some major challenges for geophysicists and structural geologists using three-dimensional boundary element method codes (3D-BEM) are: (1) reducing the amount of memory required to solve large and dense systems and (2) incorporation of inequality constraints such as traction inequality constraints (TIC) and displacement inequality constraints (DIC). The latter serves two purposes. First, for example, inequality constraints can be used to simulate frictional slip (using TIC). Second, these constraints can prevent element interpenetration while allowing opening mode (using DIC). We have developed a method that simultaneously incorporates both types of functionality of the inequality constraints. We show that the use of an appropriate iterative solver not only avoids the allocation of significant memory for solving the system (allowing very large model computation and simplifying parallelization on multi-core processors), but also admits interesting features such as natural incorporation of TICs and DICs. Compared to other techniques of contact management (e.g., Lagrange multipliers, penalty method, or complementarity problem), this new simple methodology, which does not use any incremental trial-and-error procedures, brings more flexibility, while making the system more stable and less subject to round-off errors without any computational overhead. We provide validations and comparisons of the inequality constraints implementation using 2D analytical and numerical solutions.
ISSN: 1420-0597

hal-00561035
https://hal.archives-ouvertes.fr/hal-00561035
DOI : 10.1007/s10596-009-9170-x