A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

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

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 this paper, we consider a class of Forward--Backward (FB) splitting methods that includes
several variants (eg, inertial schemes, FISTA) for minimizing the sum of two proper convex …

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 …

Solving inverse problems with iterative algorithms is popular, especially for large data. Due
to time constraints, the number of possible iterations is usually limited, potentially affecting …

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 …