We propose a geometric framework to describe and analyse a wide array of operator
splitting methods for solving monotone inclusion problems. The initial inclusion problem …

In a Hilbert space, we provide a fast dynamic approach to the hierarchical minimization
problem which consists in finding the minimum norm solution of a convex minimization …

We propose new primal-dual decomposition algorithms for solving systems of inclusions
involving sums of linearly composed maximally monotone operators. The principal …

In a Hilbertian framework, for the minimization of a general convex differentiable function f,
we introduce new inertial dynamics and algorithms that generate trajectories and iterates …

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 backward–forward algorithm as a splitting method to solve
structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has …

Resolvents of set-valued operators play a central role in various branches of mathematics
and in particular in the design and the analysis of splitting algorithms for solving monotone …

We investigate the strong convergence properties of a Nesterov type algorithm with two
Tikhonov regularization terms in connection to the minimization problem of a smooth convex …

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in
Hilbert spaces share the common feature to guarantee for the generated sequences in …

We propose a novel approach to monotone operator splitting based on the notion of a
saddle operator. Under investigation is a highly structured multivariate monotone inclusion …