Related papers: Resolvent splitting with minimal lifting for compo…

Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…

In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is…

We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental…

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend…

We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…

We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…

We present a method for solving linearly constrained convex optimization problems, which is based on the application of known algorithms for finding zeros of the sum of two monotone operators (presented by Eckstein and Svaiter) to the dual…

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…

Monotone operator splitting is a powerful paradigm that facilitates parallel processing for optimization problems where the cost function can be split into two convex functions. We propose a generalized form of monotone operator splitting…

Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…

The nonlinear, or warped, resolvent recently explored by Giselsson and B\`ui-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents,…

We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of…

This paper presents an in-depth analysis of a parametrized version of the resolvent composition, an operation that combines a set-valued operator and a linear operator. We provide new properties and examples, and show that resolvent…

We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…