In a real Hilbert space H, in order to develop fast optimization methods, we analyze the
asymptotic behavior, as time t tends to infinity, of a large class of autonomous dissipative …

We revisit the Ravine method of Gelfand and Tsetlin from a dynamical system perspective,
study its convergence properties, and highlight its similarities and differences with the …

In a Hilbert setting, we develop a gradient-based dynamic approach for fast solving convex
optimization problems. By applying time scaling, averaging, and perturbation techniques to …

This paper proposes an inertial Bregman proximal gradient method for minimizing the sum
of two possibly nonconvex functions. This method includes two different inertial steps and …

This paper deals with a second order dynamical system with a Tikhonov regularization term
in connection to the minimization problem of a convex Fréchet differentiable function. The …

In the history of first-order algorithms, Nesterov's accelerated gradient descent (NAG) is one
of the milestones. However, the cause of the acceleration has been a mystery for a long …

Second-order continuous-time dissipative dynamical systems with viscous and Hessian
driven damping have inspired effective first-order algorithms for solving convex optimization …

This paper deals with a second order dynamical system with vanishing damping that
contains a Tikhonov regularization term, in connection to the minimization problem of a …

Our approach is part of the close link between continuous dissipative dynamical systems
and optimization algorithms. We aim to solve convex minimization problems by means of …

In a Hilbert setting, for convex differentiable optimization, we develop a general framework
for adaptive accelerated gradient methods. They are based on damped inertial dynamics …