]. F. Alvarez, ]. F. Alvarez-alvarez, and H. Attouch, On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces, SIAM Journal on Control and Optimization, vol.38, issue.4, pp.1102-1119, 2000.
DOI : 10.1137/S0363012998335802

H. Attouch and A. Cabot, Convergence Rates of Inertial Forward-Backward Algorithms, SIAM Journal on Optimization, vol.28, issue.1, pp.849-874, 2018.
DOI : 10.1137/17M1114739

URL : https://hal.archives-ouvertes.fr/hal-01453170

H. Attouch and A. Cabot, Convergence of damped inertial dynamics governed by regularized maximally monotone operators, Journal of Differential Equations, vol.264, issue.12, pp.7138-7182, 2018.
DOI : 10.1016/j.jde.2018.02.017

URL : https://hal.archives-ouvertes.fr/hal-01648383

H. Attouch and A. Cabot, Convergence of a relaxed inertial proximal algorithm for maximally monotone operators, p.1708905, 2018.
DOI : 10.1007/s10107-018-1252-x

URL : https://hal.archives-ouvertes.fr/hal-01708905

H. Attouch, Z. Chbani, J. Peypouquet, and P. Redont, Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity, Mathematical Programming, vol.23, issue.3, pp.123-175, 2018.
DOI : 10.1137/110844805

H. Attouch and J. Peypouquet, The Rate of Convergence of Nesterov's Accelerated Forward-Backward Method is Actually Faster Than $1/k^2$, SIAM Journal on Optimization, vol.26, issue.3
DOI : 10.1137/15M1046095

URL : http://arxiv.org/pdf/1510.08740

H. Attouch and J. Peypouquet, Convergence of inertial dynamics and proximal algorithms governed by maximal monotone operators, Math. Program., Ser. B, 2018.
DOI : 10.1007/s10107-018-1252-x

URL : http://arxiv.org/pdf/1705.03803

J. Aujol and . Ch, Stability of Over-Relaxations for the Forward-Backward Algorithm, Application to FISTA, SIAM Journal on Optimization, vol.25, issue.4, pp.25-2408, 2015.
DOI : 10.1137/140994964

URL : https://hal.archives-ouvertes.fr/hal-01163432

J. Aujol, . Ch, A. Dossal, and . Rondepierre, Optimal convergence rates for Nesterov acceleration, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01786117

H. Bauschke and P. Combettes, 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-01517477

A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009.
DOI : 10.1137/080716542

URL : http://ie.technion.ac.il/%7Ebecka/papers/finalicassp2009.pdf

P. Bégout, J. Bolte, and M. A. Jendoubi, On damped second-order gradient systems, Journal of Differential Equations, vol.259, issue.7, pp.3115-3143, 2015.
DOI : 10.1016/j.jde.2015.04.016

R. I. Bot and E. R. Csetnek, Second Order Forward-Backward Dynamical Systems For Monotone Inclusion Problems, SIAM Journal on Control and Optimization, vol.54, issue.3, pp.1423-1443, 2016.
DOI : 10.1137/15M1012657

H. Brézis, Opérateurs maximaux monotones dans les espaces de Hilbert etéquationsetéquations d'´ evolution, Lecture Notes 5, 1972.

A. Chambolle and . Ch, On the Convergence of the Iterates of the ???Fast Iterative Shrinkage/Thresholding Algorithm???, Journal of Optimization Theory and Applications, vol.155, issue.2, pp.968-982, 2015.
DOI : 10.1007/978-1-4419-9467-7

Y. Drori and M. Teboulle, Performance of first-order methods for smooth convex minimization: a novel approach, Mathematical Programming, vol.38, issue.1, pp.451-482, 2014.
DOI : 10.1137/1038003

URL : http://arxiv.org/pdf/1206.3209

J. Eckstein and D. P. Bertsekas, On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.29, issue.1, pp.293-318, 1992.
DOI : 10.2140/pjm.1970.33.209

URL : http://web.mit.edu/afs/athena.mit.edu/user/d/i/dimitrib/www/Eckstein_Bertsekas_D-R.pdf

F. Iutzeler and J. M. Hendrickx, A generic online acceleration scheme for optimization algorithms via relaxation and inertia, Optimization Methods and Software, vol.27, issue.2, 2017.
DOI : 10.1007/s10107-016-1009-3

URL : https://hal.archives-ouvertes.fr/hal-01685717

F. Iutzeler and J. Malick, On the Proximal Gradient Algorithm with Alternated Inertia, Journal of Optimization Theory and Applications, vol.7, issue.2, pp.688-710, 2018.
DOI : 10.1007/978-3-319-41589-5_7

URL : https://hal.archives-ouvertes.fr/hal-01685859

D. Kim and J. A. Fessler, Optimized first-order methods for smooth convex minimization, Mathematical Programming, vol.125, issue.2, pp.81-107, 2016.
DOI : 10.1007/s10107-010-0394-2

URL : http://europepmc.org/articles/pmc5067109?pdf=render

J. Liang, J. Fadili, and G. Peyré, Local linear convergence of forward-backward under partial smoothness, Advances in Neural Information Processing Systems, pp.1970-1978, 2014.
DOI : 10.1007/978-3-319-18461-6_51

URL : https://hal.archives-ouvertes.fr/hal-01150460

P. Maingé, Convergence theorems for inertial KM-type algorithms, Journal of Computational and Applied Mathematics, vol.219, issue.1, pp.223-236, 2008.
DOI : 10.1016/j.cam.2007.07.021

Y. Nesterov, A method of solving a convex programming problem with convergence rate, Soviet Mathematics Doklady, pp.372-376, 1983.

Y. Nesterov, Introductory lectures on convex optimization: A basic course, of Applied Optimization, 2004.
DOI : 10.1007/978-1-4419-8853-9

Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, vol.73, issue.4, pp.591-597, 1967.
DOI : 10.1090/S0002-9904-1967-11761-0

N. Parikh and S. Boyd, Proximal algorithms, Foundations and trends in optimization, pp.123-231, 2013.

J. Peypouquet, Convex optimization in normed spaces: theory, methods and examples, 2015.
DOI : 10.1007/978-3-319-13710-0

B. T. Polyak, Some methods of speeding up the convergence of iteration methods, USSR Computational Mathematics and Mathematical Physics, vol.4, issue.5, pp.1-17, 1964.
DOI : 10.1016/0041-5553(64)90137-5

W. Su, S. Boyd, and E. J. Candès, A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights, Journal of Machine Learning Research, vol.17, pp.1-43, 2016.

S. Villa, S. Salzo, L. Baldassarres, and A. Verri, Accelerated and Inexact Forward-Backward Algorithms, SIAM Journal on Optimization, vol.23, issue.3, pp.1607-1633, 2013.
DOI : 10.1137/110844805

URL : http://www.optimization-online.org/DB_FILE/2011/08/3132.pdf

A. Institut-montpelliérain and . Grothendieck, 34095 Montpellier cedex 5, France E-mail address: hedy.attouch@univ-montp2, fr Institut de Mathématiques de Bourgogne, UMR 5584 CNRS