Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3
ESAIM: COCV, 25 (2019) 2
Published online: 2019-04-08
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Strong and Fast Convergences for Damping, Scaling and Tikhonov Regularization
Hassan RiahiJournal of Optimization Theory and Applications 208 (1) (2026)
https://doi.org/10.1007/s10957-025-02842-x
Singular Perturbation Analysis of Accelerated Inertial Systems for Non-Potential Operators in the High-Damping Regime
Samir Adly, Kouegnon D. Mitchozounnou and Olivier ProtJournal of Optimization Theory and Applications 209 (2) (2026)
https://doi.org/10.1007/s10957-026-02985-5
Stochastic monotone inclusion with closed loop distributions
Hamza Ennaji, Jalal Fadili and Hedy AttouchEvolution Equations and Control Theory 17 140 (2026)
https://doi.org/10.3934/eect.2025022
Fast convergence of primal-dual dynamical systems with implicit Hessian damping and Tikhonov regularization
Hong-lu Li, Xin He and Yi-bin XiaoCommunications in Nonlinear Science and Numerical Simulation 161 110051 (2026)
https://doi.org/10.1016/j.cnsns.2026.110051
Double momentum projected gradient method for large-scale machine learning and signal processing
Jian-Wen Peng, Abubakar Adamu, Yekini Shehu and Jen-Chih YaoJournal of Applied Mathematics and Computing 72 (4) (2026)
https://doi.org/10.1007/s12190-026-02803-1
Near-optimal Closed-loop Method via Lyapunov Damping
Severin Maier, Camille Castera and Peter OchsJournal of Optimization Theory and Applications 208 (3) (2026)
https://doi.org/10.1007/s10957-025-02906-y
From inertial systems to proximal flows: The large damping limit of implicit Hessian-driven dynamics
Samir Adly, Denis K. Mitchozounnou and Olivier ProtEvolution Equations and Control Theory 17 201 (2026)
https://doi.org/10.3934/eect.2025072
On a class of second-order dynamical systems involving viscous and Hessian-driven damping
Dang-Khoa NguyenEvolution Equations and Control Theory 17 231 (2026)
https://doi.org/10.3934/eect.2025075
Inertial Dynamical Systems and Accelerated Algorithms with Implicit Hessian-Driven Damping for Nonconvex Optimization
Zeying Gao, Xiangkai Sun and Liang HeJournal of Optimization Theory and Applications 210 (1) (2026)
https://doi.org/10.1007/s10957-026-03052-9
Symplectic discretization approach for developing new proximal point algorithm
Ya-xiang Yuan and Yi ZhangComputational Optimization and Applications 93 (2) 651 (2026)
https://doi.org/10.1007/s10589-025-00728-2
An accelerated lyapunov function for Polyak’s Heavy-ball on convex quadratics
Antonio OrvietoOptimization Letters 19 (2) 307 (2025)
https://doi.org/10.1007/s11590-024-02119-8
Fast symplectic integrator for Nesterov-type acceleration method
Shin-itiro Goto and Hideitsu HinoJapan Journal of Industrial and Applied Mathematics 42 (1) 331 (2025)
https://doi.org/10.1007/s13160-024-00680-4
A General Mixed-Order Primal-Dual Dynamical System with Tikhonov Regularization
Hong-lu Li, Rong Hu, Xin He and Yi-bin XiaoJournal of Optimization Theory and Applications 207 (2) (2025)
https://doi.org/10.1007/s10957-025-02798-y
A unified differential equation solver approach for separable convex optimization: Splitting, acceleration and nonergodic rate
Hao Luo and Zihang ZhangMathematics of Computation 94 (356) 3009 (2025)
https://doi.org/10.1090/mcom/4063
THE SECOND-ORDER DIFFERENTIAL EQUATION METHOD FOR SOLVING THE VARIATIONAL INEQUALITY PROBLEM
Danna Jia, Li Wang, Juhe Sun and Huiting ZhuangJournal of Applied Analysis & Computation 14 (2) 760 (2024)
https://doi.org/10.11948/20230084
Fast convex optimization via a third-order in time evolution equation: TOGES-V an improved version of TOGES*
Hedy Attouch, Zaki Chbani and Hassan RiahiOptimization 73 (3) 575 (2024)
https://doi.org/10.1080/02331934.2022.2119084
Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions
Radu Ioan Boţ and David Alexander HulettJournal of Dynamics and Differential Equations 36 (1) 727 (2024)
https://doi.org/10.1007/s10884-022-10160-3
Fast Convex Optimization via Differential Equation with Hessian-Driven Damping and Tikhonov Regularization
Gangfan Zhong, Xiaozhe Hu, Ming Tang and Liuqiang ZhongJournal of Optimization Theory and Applications 203 (1) 42 (2024)
https://doi.org/10.1007/s10957-024-02462-x
Comparative analysis of accelerated gradient algorithms for convex optimization: high and super resolution ODE approach
Samir Adly, Hedy Attouch and Jalal FadiliOptimization 1 (2024)
https://doi.org/10.1080/02331934.2024.2422563
Complexity Analysis Based on Tuning the Viscosity Parameter of the Su-Boyd-Candès Inertial Gradient Dynamics
Samir Adly and Hedy AttouchSet-Valued and Variational Analysis 32 (2) (2024)
https://doi.org/10.1007/s11228-024-00720-8
A Second Order Primal–Dual Dynamical System for a Convex–Concave Bilinear Saddle Point Problem
Xin He, Rong Hu and Yaping FangApplied Mathematics & Optimization 89 (2) (2024)
https://doi.org/10.1007/s00245-023-10102-5
Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems
Konstantin Sonntag and Sebastian PeitzJournal of Optimization Theory and Applications 201 (2) 539 (2024)
https://doi.org/10.1007/s10957-024-02389-3
Optimal convergence rate of inertial gradient system with flat geometries and perturbations
Jia-Hui Cai and Jun-Ren LuoEvolution Equations and Control Theory (2024)
https://doi.org/10.3934/eect.2024002
A Systematic Approach to Lyapunov Analyses of Continuous-Time Models in Convex Optimization
Céline Moucer, Adrien Taylor and Francis BachSIAM Journal on Optimization 33 (3) 1558 (2023)
https://doi.org/10.1137/22M1498486
On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping
Hedy Attouch, Jalal Fadili and Vyacheslav KungurtsevEvolution Equations and Control Theory 12 (1) 71 (2023)
https://doi.org/10.3934/eect.2022022
Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven damping
Hedy Attouch, Zaki Chbani, Jalal Fadili and Hassan RiahiOptimization 72 (5) 1199 (2023)
https://doi.org/10.1080/02331934.2021.2009828
Fast Convergence of Inertial Gradient Dynamics with Multiscale Aspects
Haixin Ren, Bin Ge and Xiangwu ZhugeJournal of Optimization Theory and Applications 196 (2) 461 (2023)
https://doi.org/10.1007/s10957-022-02124-w
Accelerated differential inclusion for convex optimization
Hao LuoOptimization 72 (5) 1139 (2023)
https://doi.org/10.1080/02331934.2021.2002327
Optimal Convergence Rates for Damped Inertial Gradient Dynamics with Flat Geometries
Jun-Ren Luo and Ti-Jun XiaoApplied Mathematics & Optimization 87 (3) (2023)
https://doi.org/10.1007/s00245-023-09966-4
Time Rescaling of a Primal-Dual Dynamical System with Asymptotically Vanishing Damping
David Alexander Hulett and Dang-Khoa NguyenApplied Mathematics & Optimization 88 (2) (2023)
https://doi.org/10.1007/s00245-023-09999-9
A Second-Order Projected Primal-Dual Dynamical System for Distributed Optimization and Learning
Xiaoxuan Wang, Shaofu Yang, Zhenyuan Guo and Tingwen HuangIEEE Transactions on Neural Networks and Learning Systems 34 (9) 6568 (2023)
https://doi.org/10.1109/TNNLS.2021.3127883
Dynamical Primal-Dual Nesterov Accelerated Method and Its Application to Network Optimization
Xianlin Zeng, Jinlong Lei and Jie ChenIEEE Transactions on Automatic Control 68 (3) 1760 (2023)
https://doi.org/10.1109/TAC.2022.3152720
196 (2023)
https://doi.org/10.1109/NTCI60157.2023.10403724
1 (2023)
https://doi.org/10.1109/IAI59504.2023.10327562
On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping
Szilárd Csaba LászlóJournal of Differential Equations 362 355 (2023)
https://doi.org/10.1016/j.jde.2023.03.014
Accelerated dynamics with dry friction via time scaling and averaging of doubly nonlinear evolution equations
Samir Adly and Hedy AttouchNonlinear Analysis: Hybrid Systems 50 101402 (2023)
https://doi.org/10.1016/j.nahs.2023.101402
Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization
Xin Qu and Wei BianComputational Optimization and Applications 83 (1) 287 (2022)
https://doi.org/10.1007/s10589-022-00388-6
A control-theoretic perspective on optimal high-order optimization
Tianyi Lin and Michael I. JordanMathematical Programming 195 (1-2) 929 (2022)
https://doi.org/10.1007/s10107-021-01721-3
From differential equation solvers to accelerated first-order methods for convex optimization
Hao Luo and Long ChenMathematical Programming 195 (1-2) 735 (2022)
https://doi.org/10.1007/s10107-021-01713-3
First-order optimization algorithms via inertial systems with Hessian driven damping
Hedy Attouch, Zaki Chbani, Jalal Fadili and Hassan RiahiMathematical Programming 193 (1) 113 (2022)
https://doi.org/10.1007/s10107-020-01591-1
From the Ravine Method to the Nesterov Method and Vice Versa: A Dynamical System Perspective
Hedy Attouch and Jalal FadiliSIAM Journal on Optimization 32 (3) 2074 (2022)
https://doi.org/10.1137/22M1474357
Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition
Vassilis Apidopoulos, Nicolò Ginatta and Silvia VillaJournal of Global Optimization 84 (3) 563 (2022)
https://doi.org/10.1007/s10898-022-01164-w
Potential Function-Based Framework for Minimizing Gradients in Convex and Min-Max Optimization
Jelena Diakonikolas and Puqian WangSIAM Journal on Optimization 32 (3) 1668 (2022)
https://doi.org/10.1137/21M1395302
Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics
Hedy Attouch, Zaki Chbani, Jalal Fadili and Hassan RiahiJournal of Optimization Theory and Applications 193 (1-3) 704 (2022)
https://doi.org/10.1007/s10957-021-01859-2
Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling
Hedy Attouch, Aïcha Balhag, Zaki Chbani and Hassan RiahiEvolution Equations & Control Theory 11 (2) 487 (2022)
https://doi.org/10.3934/eect.2021010
First-order inertial algorithms involving dry friction damping
Samir Adly and Hedy AttouchMathematical Programming 193 (1) 405 (2022)
https://doi.org/10.1007/s10107-020-01613-y
Fast convex optimization via a third-order in time evolution equation
Hedy Attouch, Zaki Chbani and Hassan RiahiOptimization 71 (5) 1275 (2022)
https://doi.org/10.1080/02331934.2020.1764953
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration
Abhinav Sharma, K. Lakshmanan, Ruchir Gupta and Atul GuptaIEEE Access 9 113489 (2021)
https://doi.org/10.1109/ACCESS.2021.3103767
A second-order adaptive Douglas–Rachford dynamic method for maximal $$\alpha $$-monotone operators
Ming Zhu, Rong Hu and Ya-Ping FangJournal of Fixed Point Theory and Applications 23 (2) (2021)
https://doi.org/10.1007/s11784-021-00862-4
Analysing human-computer interaction behaviour in human resource management system based on artificial intelligence technology
Yuegang Song and Ruibing WuKnowledge Management Research & Practice 1 (2021)
https://doi.org/10.1080/14778238.2021.1955630
Tikhonov regularization of a second order dynamical system with Hessian driven damping
Radu Ioan Boţ, Ernö Robert Csetnek and Szilárd Csaba LászlóMathematical Programming 189 (1-2) 151 (2021)
https://doi.org/10.1007/s10107-020-01528-8
Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping
Radu Ioan Boţ and Dang-Khoa NguyenJournal of Differential Equations 303 369 (2021)
https://doi.org/10.1016/j.jde.2021.09.021
Convergence rates for an inertial algorithm of gradient type associated to a smooth non-convex minimization
Szilárd Csaba LászlóMathematical Programming 190 (1-2) 285 (2021)
https://doi.org/10.1007/s10107-020-01534-w
On the convergence of a class of inertial dynamical systems with Tikhonov regularization
Bo Xu and Bo WenOptimization Letters 15 (6) 2025 (2021)
https://doi.org/10.1007/s11590-020-01663-3
Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems
Xin He, Rong Hu and Ya Ping FangSIAM Journal on Control and Optimization 59 (5) 3278 (2021)
https://doi.org/10.1137/20M1355379
Tikhonov Regularization of a Perturbed Heavy Ball System with Vanishing Damping
Cristian Daniel Alecsa and Szilárd Csaba LászlóSIAM Journal on Optimization 31 (4) 2921 (2021)
https://doi.org/10.1137/20M1382027
Generalized Momentum-Based Methods: A Hamiltonian Perspective
Jelena Diakonikolas and Michael I. JordanSIAM Journal on Optimization 31 (1) 915 (2021)
https://doi.org/10.1137/20M1322716
Continuous Newton-like Inertial Dynamics for Monotone Inclusions
Hedy Attouch and Szilárd Csaba LászlóSet-Valued and Variational Analysis (2020)
https://doi.org/10.1007/s11228-020-00564-y
Convergence Rate of Inertial Proximal Algorithms with General Extrapolation and Proximal Coefficients
Hedy Attouch, Zaki Chbani and Hassan RiahiVietnam Journal of Mathematics 48 (2) 247 (2020)
https://doi.org/10.1007/s10013-020-00399-y
Convergence Rates of Damped Inertial Dynamics under Geometric Conditions and Perturbations
O. Sebbouh, Ch. Dossal and A. RondepierreSIAM Journal on Optimization 30 (3) 1850 (2020)
https://doi.org/10.1137/19M1272767
Continuous Dynamics Related to Monotone Inclusions and Non-Smooth Optimization Problems
Ernö Robert CsetnekSet-Valued and Variational Analysis 28 (4) 611 (2020)
https://doi.org/10.1007/s11228-020-00548-y
773 (2020)
https://doi.org/10.23919/ACC45564.2020.9147733
Applying FISTA to optimization problems (with or) without minimizers
Heinz H. Bauschke, Minh N. Bui and Xianfu WangMathematical Programming 184 (1-2) 349 (2020)
https://doi.org/10.1007/s10107-019-01415-x
Fast Proximal Methods via Time Scaling of Damped Inertial Dynamics
Hedy Attouch, Zaki Chbani and Hassan RiahiSIAM Journal on Optimization 29 (3) 2227 (2019)
https://doi.org/10.1137/18M1230207
Optimal Convergence Rates for Nesterov Acceleration
Jean-Francois Aujol, Charles Dossal and Aude RondepierreSIAM Journal on Optimization 29 (4) 3131 (2019)
https://doi.org/10.1137/18M1186757
Proximal alternating penalty algorithms for nonsmooth constrained convex optimization
Quoc Tran-DinhComputational Optimization and Applications 72 (1) 1 (2019)
https://doi.org/10.1007/s10589-018-0033-z
Splitting Algorithms, Modern Operator Theory, and Applications
Hedy Attouch and Juan PeypouquetSplitting Algorithms, Modern Operator Theory, and Applications 1 (2019)
https://doi.org/10.1007/978-3-030-25939-6_1
Inertial Forward–Backward Algorithms with Perturbations: Application to Tikhonov Regularization
Hedy Attouch, Alexandre Cabot, Zaki Chbani and Hassan RiahiJournal of Optimization Theory and Applications 179 (1) 1 (2018)
https://doi.org/10.1007/s10957-018-1369-3