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:

Stochastic monotone inclusion with closed loop distributions

Hamza Ennaji, Jalal Fadili and Hedy Attouch
Evolution Equations and Control Theory (2025)
https://doi.org/10.3934/eect.2025022

A unified differential equation solver approach for separable convex optimization: Splitting, acceleration and nonergodic rate

Hao Luo and Zihang Zhang
Mathematics of Computation (2025)
https://doi.org/10.1090/mcom/4063

Fast symplectic integrator for Nesterov-type acceleration method

Shin-itiro Goto and Hideitsu Hino
Japan Journal of Industrial and Applied Mathematics 42 (1) 331 (2025)
https://doi.org/10.1007/s13160-024-00680-4

Complexity Analysis Based on Tuning the Viscosity Parameter of the Su-Boyd-Candès Inertial Gradient Dynamics

Samir Adly and Hedy Attouch
Set-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 Fang
Applied 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 Peitz
Journal of Optimization Theory and Applications 201 (2) 539 (2024)
https://doi.org/10.1007/s10957-024-02389-3

THE SECOND-ORDER DIFFERENTIAL EQUATION METHOD FOR SOLVING THE VARIATIONAL INEQUALITY PROBLEM

Danna Jia, Li Wang, Juhe Sun and Huiting Zhuang
Journal 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 Riahi
Optimization 73 (3) 575 (2024)
https://doi.org/10.1080/02331934.2022.2119084

Optimal convergence rate of inertial gradient system with flat geometries and perturbations

Jia-Hui Cai and Jun-Ren Luo
Evolution Equations and Control Theory (2024)
https://doi.org/10.3934/eect.2024002

Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions

Radu Ioan Boţ and David Alexander Hulett
Journal 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 Zhong
Journal 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 Fadili
Optimization 1 (2024)
https://doi.org/10.1080/02331934.2024.2422563

Accelerated dynamics with dry friction via time scaling and averaging of doubly nonlinear evolution equations

Samir Adly and Hedy Attouch
Nonlinear Analysis: Hybrid Systems 50 101402 (2023)
https://doi.org/10.1016/j.nahs.2023.101402

On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping

Hedy Attouch, Jalal Fadili and Vyacheslav Kungurtsev
Evolution 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 Riahi
Optimization 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 Zhuge
Journal of Optimization Theory and Applications 196 (2) 461 (2023)
https://doi.org/10.1007/s10957-022-02124-w

On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping

Szilárd Csaba László
Journal of Differential Equations 362 355 (2023)
https://doi.org/10.1016/j.jde.2023.03.014

A Systematic Approach to Lyapunov Analyses of Continuous-Time Models in Convex Optimization

Céline Moucer, Adrien Taylor and Francis Bach
SIAM Journal on Optimization 33 (3) 1558 (2023)
https://doi.org/10.1137/22M1498486

Time Rescaling of a Primal-Dual Dynamical System with Asymptotically Vanishing Damping

David Alexander Hulett and Dang-Khoa Nguyen
Applied 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 Huang
IEEE 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 Chen
IEEE Transactions on Automatic Control 68 (3) 1760 (2023)
https://doi.org/10.1109/TAC.2022.3152720

Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization

Xin Qu and Wei Bian
Computational Optimization and Applications 83 (1) 287 (2022)
https://doi.org/10.1007/s10589-022-00388-6

From the Ravine Method to the Nesterov Method and Vice Versa: A Dynamical System Perspective

Hedy Attouch and Jalal Fadili
SIAM Journal on Optimization 32 (3) 2074 (2022)
https://doi.org/10.1137/22M1474357

Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling

Hedy Attouch, Aïcha Balhag, Zaki Chbani and Hassan Riahi
Evolution Equations & Control Theory 11 (2) 487 (2022)
https://doi.org/10.3934/eect.2021010

Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics

Hedy Attouch, Zaki Chbani, Jalal Fadili and Hassan Riahi
Journal of Optimization Theory and Applications 193 (1-3) 704 (2022)
https://doi.org/10.1007/s10957-021-01859-2

Potential Function-Based Framework for Minimizing Gradients in Convex and Min-Max Optimization

Jelena Diakonikolas and Puqian Wang
SIAM Journal on Optimization 32 (3) 1668 (2022)
https://doi.org/10.1137/21M1395302

Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition

Vassilis Apidopoulos, Nicolò Ginatta and Silvia Villa
Journal of Global Optimization 84 (3) 563 (2022)
https://doi.org/10.1007/s10898-022-01164-w

First-order optimization algorithms via inertial systems with Hessian driven damping

Hedy Attouch, Zaki Chbani, Jalal Fadili and Hassan Riahi
Mathematical Programming 193 (1) 113 (2022)
https://doi.org/10.1007/s10107-020-01591-1

Convergence rates for an inertial algorithm of gradient type associated to a smooth non-convex minimization

Szilárd Csaba László
Mathematical Programming 190 (1-2) 285 (2021)
https://doi.org/10.1007/s10107-020-01534-w

Tikhonov Regularization of a Perturbed Heavy Ball System with Vanishing Damping

Cristian Daniel Alecsa and Szilárd Csaba László
SIAM Journal on Optimization 31 (4) 2921 (2021)
https://doi.org/10.1137/20M1382027

A second-order adaptive Douglas–Rachford dynamic method for maximal $$\alpha $$-monotone operators

Ming Zhu, Rong Hu and Ya-Ping Fang
Journal of Fixed Point Theory and Applications 23 (2) (2021)
https://doi.org/10.1007/s11784-021-00862-4

Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems

Xin He, Rong Hu and Ya Ping Fang
SIAM Journal on Control and Optimization 59 (5) 3278 (2021)
https://doi.org/10.1137/20M1355379

Tikhonov regularization of a second order dynamical system with Hessian driven damping

Radu Ioan Boţ, Ernö Robert Csetnek and Szilárd Csaba László
Mathematical Programming 189 (1-2) 151 (2021)
https://doi.org/10.1007/s10107-020-01528-8

Generalized Momentum-Based Methods: A Hamiltonian Perspective

Jelena Diakonikolas and Michael I. Jordan
SIAM Journal on Optimization 31 (1) 915 (2021)
https://doi.org/10.1137/20M1322716

Analysing human-computer interaction behaviour in human resource management system based on artificial intelligence technology

Yuegang Song and Ruibing Wu
Knowledge Management Research & Practice 1 (2021)
https://doi.org/10.1080/14778238.2021.1955630

Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping

Radu Ioan Boţ and Dang-Khoa Nguyen
Journal of Differential Equations 303 369 (2021)
https://doi.org/10.1016/j.jde.2021.09.021

Convergence Rate of Inertial Proximal Algorithms with General Extrapolation and Proximal Coefficients

Hedy Attouch, Zaki Chbani and Hassan Riahi
Vietnam 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. Rondepierre
SIAM Journal on Optimization 30 (3) 1850 (2020)
https://doi.org/10.1137/19M1272767

Fast Proximal Methods via Time Scaling of Damped Inertial Dynamics

Hedy Attouch, Zaki Chbani and Hassan Riahi
SIAM 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 Rondepierre
SIAM Journal on Optimization 29 (4) 3131 (2019)
https://doi.org/10.1137/18M1186757

Inertial Forward–Backward Algorithms with Perturbations: Application to Tikhonov Regularization

Hedy Attouch, Alexandre Cabot, Zaki Chbani and Hassan Riahi
Journal of Optimization Theory and Applications 179 (1) 1 (2018)
https://doi.org/10.1007/s10957-018-1369-3