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 this work, we propose a simple modification of the forward-backward splitting method for
finding a zero in the sum of two monotone operators. Our method converges under the same …

We discuss here the convergence of the iterates of the “Fast Iterative Shrinkage/
Thresholding Algorithm,” which is an algorithm proposed by Beck and Teboulle for …

In this paper, we propose an inertial forward-backward splitting algorithm to compute a zero
of the sum of two monotone operators, with one of the two operators being co-coercive. The …

In this paper we study an algorithm for solving a minimization problem composed of a
differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The …

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∇ …

The forward-backward algorithm is a powerful tool for solving optimization problems with an
additively separable and smooth plus nonsmooth structure. In the convex setting, a simple …

In this article, we introduce an inertial projection and contraction algorithm by combining
inertial type algorithms with the projection and contraction algorithm for solving a variational …

We propose an inertial Douglas–Rachford splitting algorithm for finding the set of zeros of
the sum of two maximally monotone operators in Hilbert spaces and investigate its …

The paper presents a fully adaptive algorithm for monotone variational inequalities. In each
iteration the method uses two previous iterates for an approximation of the local Lipschitz …