On stochastic proximal gradient algorithms. ArXiv e-prints, 1402, p.2365, 2014. ,
Familles d'op??rateurs maximaux monotones et mesurabilit??, Annali di Matematica Pura ed Applicata, Series 4, vol.276, issue.1, pp.35-111, 1979. ,
DOI : 10.2140/pjm.1968.24.525
Differential inclusions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, vol.264, 1984. ,
URL : https://hal.archives-ouvertes.fr/hal-00915425
Legendre functions and the method of random bregman projections, Journal of Convex Analysis, vol.4, issue.1, pp.27-67, 1997. ,
Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization, Mathematical Programming, pp.135-160, 1999. ,
DOI : 10.1007/s101070050083
Convex analysis and monotone operator theory in Hilbert spaces, CMS Books in Mathematics, 2011. ,
DOI : 10.1007/978-3-319-48311-5
URL : https://hal.archives-ouvertes.fr/hal-00643354
Dynamics of stochastic approximation algorithms, Séminaire de Probabilités, XXXIII, pp.1-68, 1999. ,
Stochastic approximation algorithms with constant step size whose average is cooperative, Ann. Appl. Probab, vol.9, issue.1, pp.216-241, 1999. ,
Stochastic Approximations and Differential Inclusions, SIAM Journal on Control and Optimization, vol.44, issue.1, pp.328-348, 2005. ,
DOI : 10.1137/S0363012904439301
Incremental proximal methods for large scale convex optimization, Mathematical Programming, vol.8, issue.2, pp.163-195, 2011. ,
DOI : 10.1137/S1052623495294797
URL : http://www-mit.mit.edu/dimitrib/www/Incremental_Proximal.pdf
Ergodic Convergence of a Stochastic Proximal Point Algorithm, SIAM Journal on Optimization, vol.26, issue.4, pp.2235-2260, 2016. ,
DOI : 10.1137/15M1017909
Dynamical Behavior of a Stochastic Forward???Backward Algorithm Using Random Monotone Operators, Journal of Optimization Theory and Applications, vol.7, issue.3, pp.90-120, 2016. ,
DOI : 10.1080/17442508208833217
URL : https://hal.archives-ouvertes.fr/hal-01183959
Constant step stochastic approximations involving differential inclusions: Stability, long-run convergence and applications. arXiv preprint, 2016. ,
Convex analysis and nonlinear optimization, CMS Books in Mathematics, vol.3 ,
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland mathematics studies, 1973. ,
Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, Journal of Functional Analysis, vol.18, issue.1, pp.15-26, 1975. ,
DOI : 10.1016/0022-1236(75)90027-0
Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, vol.580, 1977. ,
DOI : 10.1007/BFb0087685
Stochastic Quasi-Fej??r Block-Coordinate Fixed Point Iterations with Random Sweeping, SIAM Journal on Optimization, vol.25, issue.2, pp.1221-1248, 2015. ,
DOI : 10.1137/140971233
URL : http://arxiv.org/pdf/1404.7536
Stochastic approximations and perturbations in forwardbackward splitting for monotone operators, Pure Appl. Funct. Anal, vol.1, issue.1, pp.13-37, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01380000
Elements of topological dynamics, of Mathematics and its Applications, 1993. ,
DOI : 10.1007/978-94-015-8171-4
Bridging the gap between constant step size stochastic gradient descent and markov chains, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01565514
Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor, Mathematics of Operations Research, vol.35, issue.3, pp.624-640, 2010. ,
DOI : 10.1287/moor.1100.0455
URL : https://hal.archives-ouvertes.fr/hal-00383277
Asymptotic Behavior of a Markovian Stochastic Algorithm with Constant Step, SIAM Journal on Control and Optimization, vol.37, issue.5, pp.1456-1482, 1999. ,
DOI : 10.1137/S0363012997328610
Integrals, conditional expectations, and martingales of multivalued functions, Journal of Multivariate Analysis, vol.7, issue.1, pp.149-182, 1977. ,
DOI : 10.1016/0047-259X(77)90037-9
About properties of the mean value functional and of the continuous infimal convolution in stochastic convex analysis, pp.763-789, 1976. ,
ContributionsàContributions`Contributionsà la programmation mathématique: cas déterministe et stochastique Université de Clermont-Ferrand II, Clermont-Ferrand, Thèse présentéè a l'Université de Clermont-Ferrand II pour obtenir le grade de DocteurèsDocteurès Sciences Mathématiques, 1977. ,
Stochastic approximation and recursive algorithms and applications, Stochastic Modelling and Applied Probability, 2003. ,
Approximation et optimisation, Collection Enseignement des Sciences, issue.13, 1972. ,
Theory of random sets. Probability and its Applications, 2005. ,
DOI : 10.1007/978-1-4471-7349-6
Bases mathématiques du calcul des probabilités, Masson et Cie, ´ Editeurs, 1964. ,
Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, J. Convex Anal, vol.17, pp.3-41113, 2010. ,
Lectures on maximal monotone operators, Extracta Math, vol.12, issue.3, pp.193-230, 1997. ,
Measurable dependence of convex sets and functions on parameters, Journal of Mathematical Analysis and Applications, vol.28, issue.1, pp.4-25, 1969. ,
DOI : 10.1016/0022-247X(69)90104-8
Convex analysis. Princeton Mathematical Series, 1970. ,
On the interchange of subdifferentiation and conditional expectation for convex functionals, Stochastics, vol.137, issue.3, pp.173-182, 1982. ,
DOI : 10.1007/BFb0120750
Convergence of stochastic proximal gradient algorithm, 2014. ,
A stochastic inertial forward?backward splitting algorithm for multivariate monotone inclusions. Optimization, pp.1293-1314, 2016. ,
DOI : 10.1080/02331934.2015.1127371
URL : http://arxiv.org/pdf/1507.00848
Stochastic Approximations with Constant Step Size and Differential Inclusions, SIAM Journal on Control and Optimization, vol.51, issue.1, pp.525-555, 2013. ,
DOI : 10.1137/110844192
Stochastic Programs with Recourse II: On the Continuity of the Objective, SIAM Journal on Applied Mathematics, vol.17, issue.1, pp.98-103, 1969. ,
DOI : 10.1137/0117010