This survey article addresses the class of continuous-time systems where a system modeled
by ordinary differential equations is coupled with a static or time-varying set-valued operator …

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 …

This paper proposes an accelerated proximal point method for maximally monotone
operators. The proof is computer-assisted via the performance estimation problem …

In the framework of real Hilbert spaces, we study continuous in time dynamics as well as
numerical algorithms for the problem of approaching the set of zeros of a single-valued …

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 …

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 propose in a Hilbertian setting a second-order time-continuous dynamic
system with fast convergence guarantees to solve structured convex minimization problems …

We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-
coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's …

In a Hilbert space setting, we consider a class of inertial proximal algorithms for nonsmooth
convex optimization, with fast convergence properties. They can be obtained by time …