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 …

The celebrated Kuramoto model captures various synchronization phenomena in biological
and man-made dynamical systems of coupled oscillators. It is well known that there exists a …

We study the behavior of the trajectories of a second-order differential equation with
vanishing dam**, governed by the Yosida regularization of a maximally monotone …

In a Hilbert space HH, we study the convergence properties of a class of relaxed inertial
forward–backward algorithms. They aim to solve structured monotone inclusions of the form …

We begin by considering second order dynamical systems of the from
̈x(t)+γ(t)̇x(t)+λ(t)B(x(t))=0, where B:\calH→\calH is a cocoercive operator defined on a real …

In a Hilbert space HH, given A: H → 2^ HA: H→ 2 H a maximally monotone operator, we
study the convergence properties of a general class of relaxed inertial proximal algorithms …

We analyze continuous-time models of accelerated gradient methods through deriving
conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics …

In this paper, we introduce three new inertial-like Bregman projection methods with a
nonmonotone adaptive step-size for solving quasi-monotone variational inequalities in real …

The introduction of the Hessian dam** in the continuous version of Nesterov's accelerated
gradient method provides, by temporal discretization, fast proximal gradient algorithms …

We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for
approaching the set of zeros of the sum of a maximally monotone operator and a single …