Warped proximal iterations for monotone inclusions

Monotone Iterations for Eliptic Variational Inequalities

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

Split Monotone Variational Inclusions

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...

The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions

The aim of this paper is to investigate the asymptotic behavior of an inertial alternating algorithm based on the composition of resolvents of monotone operators. The proposed algorithm is a generalization of those proposed in [2] and [3]. As a special case, we also recover the classical alternating minimization algorithm [1], which itself is a natural extension of the alternating projection al...

Stochastic Forward-Backward Splitting for Monotone Inclusions

We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward-backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as L. Rosasco DIBRIS, Univ...