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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

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

This paper studies a class of monotone inclusion problems in a real Hilbert space involving the sum of three operators, where two are maximal monotone and the third is cocoercive. The Davis--Yin three-operator splitting method extends the…

Optimization and Control · Mathematics 2026-05-14 Maoran Wang , Zijun Xia , Xingju Cai

We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…

Optimization and Control · Mathematics 2024-11-20 Patrick L. Combettes

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

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

We propose a new class of primal-dual Fejer monotone algorithms for solving systems of com- posite monotone inclusions. Our construction is inspired by a framework used by Eckstein and Svaiter for the basic problem of finding a zero of the…

Optimization and Control · Mathematics 2014-10-07 Abdullah Alotaibi , Patrick L. Combettes , N. Shahzad

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…

Optimization and Control · Mathematics 2021-09-24 Heinz H. Bauschke , Shambhavi Singh , Xianfu Wang

In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term.…

Optimization and Control · Mathematics 2024-09-27 Fernando Roldán

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…

Machine Learning · Computer Science 2025-05-08 İrfan Işik , Ibrahim Karahan , Okan Erkaymaz

In this paper we propose a resolvent splitting with minimal lifting for finding a zero of the sum of $n\ge 2$ maximally monotone operators involving the composition with a linear bounded operator. The resolvent of each monotone operator,…

Optimization and Control · Mathematics 2022-07-28 Luis M. Briceño-Arias

In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…

Optimization and Control · Mathematics 2022-01-05 Radu Ioan Bot , David Alexander Hulett

We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the…

Optimization and Control · Mathematics 2014-03-31 Radu Ioan Bot , Ernö Robert Csetnek , Christopher Hendrich

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…

Numerical Analysis · Mathematics 2025-01-14 Jan Lorenz , Tom Zwerschke , Michael Günther , Kevin Schäfers

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 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

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…

Optimization and Control · Mathematics 2013-07-22 Cameron Talischi , Glaucio H. Paulino

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…

Optimization and Control · Mathematics 2015-07-31 Damek Davis

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

Optimization and Control · Mathematics 2015-11-30 Patrick L. Combettes , Jonathan Eckstein

The three-operators splitting algorithm is a popular operator splitting method for finding the zeros of the sum of three maximally monotone operators, with one of which is cocoercive operator. In this paper, we propose a class of inertial…

Optimization and Control · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Yang Yang