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In a Hilbert setting, we develop a gradient-based dynamic approach for fast solving convex optimization problems.
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Gelfand, I., Tsetlin, M., 1963 · 1963
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Some methods of speeding up the convergence of iteration methods
Polyak, B., 1964 · 1964
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Opérateurs maximaux monotones dans les espaces de Hilbert et équations d’évolution
Brézis, H., 1972 · 1972
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Analyse fonctionnelle, Théorie et applications
Brézis, H., 1983 · 1983
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A method of solving a convex programming problem with convergence rate 𝒪 ( 1 / k 2 ) \mathcal{O}(1/k^{2})
Nesterov, Y., 1983 · 1983
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Introduction to Optimization
Polyak, B., 1987 · 1987
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The heavy ball with friction method. the continuous dynamical system, global exploration of the local minima of a real-valued function by asymptotical analysis of a dissipative dynamical system
Attouch, H., Goudou, X., Redont, P., 2000 · 2000
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Smooth minimization of non-smooth functions
Nesterov, Y., 2005 · 2005
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Beck, A., Teboulle, M., 2009 · 2009
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On the long time behavior of second order differential equations with asymptotically small dissipation
Cabot, A., Engler, H., Gadat, S., 2009 · 2009
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Asymptotic behavior of coupled dynamical systems with multiscale aspects
Attouch, H., Czarnecki, M.O., 2010 · 2010
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A continuous dynamical Newton-like approach to solving monotone inclusions
Attouch, H., Svaiter, B.F., 2011 · 2011
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Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces
Attouch, H., Redont, P., Svaiter, B.F., 2013 · 2013
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Newton-like dynamics and forward–backward methods for structured monotone inclusions in hilbert spaces
Abbas, B., Attouch, H., Svaiter, B., 2014 · 2014
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Variational analysis in Sobolev and BV spaces. Applications to PDE’s and optimization
Attouch, H., Buttazzo, G., Michaille, G., 2014 · 2014
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Compositions and convex combinations of averaged nonexpansive operators
Combettes, P., Yamada, I., 2015 · 2014
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On the convergence of the iterates of the Fast Iterative Shrinkage Thresholding Algorithm
Chambolle, A., Dossal, C., 2015 · 2015
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The rate of convergence of nesterov’s accelerated forward-backward method is actually faster than 1 / k 2 1/k^{2}
Attouch, H., Peypouquet, J., 2016 · 2016
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Convergence of a relaxed inertial proximal algorithm for maximally monotone operators
Attouch, H., Cabot, A., 2020 · 2020
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Robust hybrid zero-order optimization algorithms with acceleration via averaging in time
Poveda, J.I., Li, N., 2021 · 2020
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Regularized nonlinear acceleration
Scieur, D., D’Aspremont, A., Bach, F., 2020 · 2020
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An extension of the second order dynamical system that models Nesterov’s convex gradient method
Alecsa, C., László, S., Pinta, T., 2021 · 2021
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Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven damping
Attouch, H., Chbani, Z., Fadili, J., Riahi, H., 2023 · 2021
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Tikhonov regularization of a second order dynamical system with Hessian driven damping
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Attouch, H., Peypouquet, J., Redont, P., 2016b · 2016
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A differential equation for modeling Nesterov’s accelerated gradient method: theory and insights
Su, W.J., Boyd, S., Candès, E.J., 2016 · 2016
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Asymptotic stabilization of inertial gradient dynamics with time-dependent viscosity
Attouch, H., Cabot, A., 2017 · 2017
Cited alongside, same era.
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Bauschke, H., Combettes, P.L., 2017 · 2017
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A dynamical system associated with the fixed points set of a nonexpansive operator
Boţ, R.I., Csetnek, E.R., 2017 · 2017
Cited alongside, same era.
Convergence rates of inertial forward-backward algorithms
Attouch, H., Cabot, A., 2018 · 2018
Cited alongside, same era.
Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
Attouch, H., Chbani, Z., Peypouquet, J., Redont, P., 2018 · 2018
Cited alongside, same era.
Boţ, R.I., Csetnek, E.R., László, S., 2021 · 2021
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Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping
Boţ, R.I., Nguyen, D.K., 2021 · 2021
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Newton-like dynamics and forward–backward methods for structured monotone inclusions in hilbert spaces
Castera, C., Bolte, J., Févotte, C., Pauwels, E., 2021 · 2021
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On monotone inclusions, acceleration and closed-loop control arXiv:arXiv:2111.08093
Lin, T., Jordan, M., 2021 · 2021
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Understanding the acceleration phenomenon via high-resolution differential equations
Shi, B., Du, S.S., Jordan, M.I., Su, W.J., 2021 · 2021
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Fast OGDA in continuous and discrete time arXiv:arXiv:2203.10947
Boţ, R.I., Csetnek, E.R., Nguyen, D.K., 2022 · 2022
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From the Ravine method to the Nesterov method and vice versa: A dynamical system perspective
Attouch, H., Fadili, J., 2022 · 2074
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