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We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…

Optimization and Control · Mathematics 2015-02-23 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each…

Optimization and Control · Mathematics 2025-11-19 Liqian Qin , Aviv Gibali , Cuijie Zhang , Yuchao Tang

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…

Optimization and Control · Mathematics 2015-07-28 Patrick L. Combettes , Jean-Christophe Pesquet

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…

Optimization and Control · Mathematics 2018-07-31 Nimit Nimana , Narin Petrot

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

Monotone inclusions involving the sum of three maximally monotone operators or more have received much attention in recent years. In this paper, we propose three splitting algorithms for finding a zero of the sum of four monotone operators,…

Optimization and Control · Mathematics 2022-04-19 Jinjian Chen , Yuchao Tang

In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive…

Optimization and Control · Mathematics 2022-02-08 Luis M. Briceño-Arias , Jinjian Chen , Fernando Roldán , Yuchao Tang

Consider the problem of finding a zero of a finite sum of maximally monotone operators, where some operators are Lipschitz continuous and the rest are potentially set-valued. We propose a forward-backward-type algorithm for this problem…

Optimization and Control · Mathematics 2025-12-16 Matthew K Tam , Liam Timms , Lele Zhang

In this paper we provide a splitting method for finding a zero of the sum of a maximally monotone operator, a lipschitzian monotone operator, and a normal cone to a closed vectorial subspace of a real Hilbert space. The problem is…

Optimization and Control · Mathematics 2014-06-25 Luis M. Briceño-Arias

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…

Optimization and Control · Mathematics 2020-09-29 Minh N. Bùi , Patrick L. Combettes

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…

Optimization and Control · Mathematics 2013-06-25 Marc Lassonde , Ludovic Nagesseur

In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical…

Optimization and Control · Mathematics 2016-10-17 Puya Latafat , Panagiotis Patrinos

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the…

Optimization and Control · Mathematics 2011-08-09 Patrick L. Combettes , Jean-Christophe Pesquet

In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…

Optimization and Control · Mathematics 2022-07-20 Luis Briceño-Arias , Fernando Roldán

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator…

Optimization and Control · Mathematics 2025-06-10 Liqian Qin , Yaxuan Zhang , Qiao-Li Dong , Michael Th. Rassias

We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that…

Optimization and Control · Mathematics 2025-04-16 Anton Åkerman , Enis Chenchene , Pontus Giselsson , Emanuele Naldi

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…

Computer Vision and Pattern Recognition · Computer Science 2014-09-15 Dirk A. Lorenz , Thomas Pock

The proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}. Both methods were proposed for solving the classic variational inequalities. In this paper, we…

Optimization and Control · Mathematics 2019-08-19 Volkan Cevher , Bang Cong Vu

We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…

Optimization and Control · Mathematics 2023-12-20 Radu Ioan Bot , Dang-Khoa Nguyen , Chunxiang Zong