Related papers: Backward-Forward-Reflected-Backward Splitting for …

We propose and study a weakly convergent variant of the forward--backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector which provides additional degrees of freedom.…

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

We introduce the first operator splitting method for composite monotone inclusions outside of Hilbert spaces. The proposed primal-dual method constructs iteratively the best Bregman approximation to an arbitrary point from the Kuhn-Tucker…

Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford…

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…

In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…

We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…

We investigate frugal splitting operators for finite sum monotone inclusion problems. These operators utilize exactly one direct or resolvent evaluation of each operator of the sum, and the splitting operator's output is dictated by linear…

This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one…

In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are…

In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relative to an active…

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…

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…

The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed convex sets to a given point in a Hilbert space. In this work, we generalize the scheme so that it…

This paper provides a new way of developing the splitting method which is used to solve the problem of finding the resolvent of the sum of maximal monotone operators in Hilbert spaces. By employing accelerated techniques developed by Davis…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

In this work, we study fixed point algorithms for finding a zero in the sum of $n\geq 2$ maximally monotone operators by using their resolvents. More precisely, we consider the class of such algorithms where each resolvent is evaluated only…

The Nonlinear Forward-Backward (NFB) algorithm, also known as warped resolvent iterations, is a splitting method for finding zeros of sums of monotone operators. In particular cases, NFB reduces to well-known algorithms such as…

We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance…