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 …

In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely
on the asymptotic behavior of an inertial system combining geometric damping with …

We first study the fast minimization properties of the trajectories of the second-order
evolution equation x¨(t)+ α tx˙(t)+ β∇ 2 Φ (x (t)) x˙(t)+∇ Φ (x (t))= 0, where Φ: H→ R is a …

Given H a real Hilbert space and Φ: H→ R a smooth C 2 function, we study the dynamical
inertial system [Formula: see text] where α and β are positive parameters. The inertial term x …

In a Hilbert space setting, in order to develop fast first-order methods for convex optimization,
we study the asymptotic convergence properties (t→+∞) of the trajectories of the inertial …

In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a
class of first-order algorithms involving inertial features. They can be interpreted as discrete …

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 …

In a Hilbert space H, we study the asymptotic behavior, as time variable t goes to+∞, of
nonautonomous gradient-like inertial dynamics, with a time-dependent viscosity coefficient …

In a Hilbert space setting H, we study the fast convergence properties as t→+∞ of the
trajectories of the second-order differential equation x¨(t)+ α tx˙(t)+∇ Φ (x (t))= g (t), where∇ …

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 …