In a Hilbert space setting ℋ, given Φ: ℋ→ ℝ a convex continuously differentiable function,
and α a positive parameter, we consider the inertial dynamic system with Asymptotic …

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

In this paper, we study the behavior of solutions of the ODE associated to Nesterov
acceleration. It is well-known since the pioneering work of Nesterov that the rate of …

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 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, 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 …

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

In a Hilbert space \mathcalH, assuming (\alpha_k) a general sequence of nonnegative
numbers, we analyze the convergence properties of the inertial forward-backward algorithm …

We derive a direct connection between Nesterov's accelerated first-order algorithm and the
Halpern fixed-point iteration scheme for approximating a solution of a co-coercive equation …

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∇ …