In a Hilbert space setting, for convex optimization, we show the convergence of the iterates
to optimal solutions for a class of accelerated first-order algorithms. They can be interpreted …

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 …

In this work, we approach the minimization of a continuously differentiable convex function
under linear equality constraints by a second-order dynamical system with asymptotically …

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 …

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a
convex function in a finite-dimensional Euclidean space. Given a function\varPhi: R^ d → R …

Let H be a real Hilbert space, and f: H→ R be a convex twice differentiable function whose
solution set argmin f is nonempty. We investigate the long time behavior of the trajectories 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 …

We propose an inertial primal-dual dynamic with damping and scaling coefficients, which
involves inertial terms both for primal and dual variables, for a linearly constrained convex …

This paper examines a perturbed heavy ball system with vanishing damping that contains a
Tikhonov regularization term in connection to the minimization problem of a convex Fréchet …