English
Related papers

Related papers: An adaptive forward-backward-forward splitting alg…

200 papers

We propose an abstract stochastic scheme for solving a broad range of monotone operator inclusion problems in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels in monotone operator splitting…

Optimization and Control · Mathematics 2026-02-13 Patrick L. Combettes , Javier I. Madariaga

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

Optimization and Control · Mathematics 2024-01-11 Vu Cong Bang , Dimitri Papadimitriou , Vu Xuan Nham

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…

Optimization and Control · Mathematics 2012-06-27 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…

Optimization and Control · Mathematics 2025-08-07 Patrick L. Combettes , Javier I. Madariaga

In this paper we focus on the convergence analysis of the forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of…

Optimization and Control · Mathematics 2016-10-17 J. Y. Bello Cruz , T. T. A. Nghia

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Optimization and Control · Mathematics 2022-02-22 Francisco J. Aragón-Artacho , Radu I. Boţ , David Torregrosa-Belén

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao

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…

Optimization and Control · Mathematics 2015-05-20 Bang Cong Vũ

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…

Optimization and Control · Mathematics 2017-02-01 Alp Yurtsever , Bang Cong Vu , Volkan Cevher

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…

Optimization and Control · Mathematics 2024-12-18 Farhana A. Simi , Matthew K. Tam

It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…

Optimization and Control · Mathematics 2018-04-30 Le Dung Muu , Phung Minh Duc , Xuan Thanh Le

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…

Numerical Analysis · Mathematics 2009-11-13 Kristian Bredies

We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…

Optimization and Control · Mathematics 2017-05-02 Saverio Salzo

In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…

Optimization and Control · Mathematics 2026-05-14 Minh N. Dao , Hung M. Phan , Matthew K. Tam , Thang D. Truong

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Optimization and Control · Mathematics 2012-06-29 Patrick L. Combettes , Bang C. Vũ

In this paper, we study inclusion problems where the involved operators may not be monotone in the classical sense. Specifically, we assume the operators to be generalized monotone, a weaker notion than classical monotonicity. This allows…

Optimization and Control · Mathematics 2025-03-12 Nam Van Tran

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…

Optimization and Control · Mathematics 2016-02-26 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…

Optimization and Control · Mathematics 2025-10-03 Anshika Anshika , Jiaxing Li , Debdas Ghosh , Xiangxiong Zhang

This work describes a new variant of projective splitting for solving maximal monotone inclusions and complicated convex optimization problems. In the new version, cocoercive operators can be processed with a single forward step per…

Optimization and Control · Mathematics 2020-08-24 Patrick R. Johnstone , Jonathan Eckstein