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The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…

Optimization and Control · Mathematics 2018-05-28 R. Díaz Millán

A gradient projection method with feasible inexact projections is proposed in the present paper. The inexact projection is performed using a relative error tolerance. Asymptotic convergence analysis and iteration-complexity bounds of the…

Optimization and Control · Mathematics 2021-01-28 Ademir A. Aguiar , Orizon P. Ferreira , Leandro F. Prudente

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

Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…

Optimization and Control · Mathematics 2024-04-23 Yonghong Yao , Lateef O. Jolaoso , Yekini Shehu

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…

Optimization and Control · Mathematics 2020-06-03 Le Thi Khanh Hien , Nicolas Gillis , Panagiotis Patrinos

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

Optimization and Control · Mathematics 2017-11-07 Renato D. C. Monteiro , Chee-Khian Sim

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

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

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…

Optimization and Control · Mathematics 2025-05-28 Ling Liang , Zusen Xu , Kim-Chuan Toh , Jia-Jie Zhu

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…

Optimization and Control · Mathematics 2017-03-03 Alfredo Iusem , Alejandro Jofré , Philip Thompson

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…

Optimization and Control · Mathematics 2018-05-31 Luis Briceño-Arias , Sergio López Rivera

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…

Numerical Analysis · Mathematics 2024-06-12 Antonio Leitão , Joel C. Rabelo , Dirk A. Lorenz , Maximilian Winkler

We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the…

Optimization and Control · Mathematics 2025-09-24 M. Marques Alves , J. E. Navarro Caballero , M. Geremia , R. T. Marcavillaca

In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…

Optimization and Control · Mathematics 2013-07-01 Sina Khoshfetrat Pakazad , Martin S. Andersen , Anders Hansson

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…

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

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

Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for…

Optimization and Control · Mathematics 2020-09-29 Hui Yu , Chunxiang Zong , Yuchao Tang

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…

Optimization and Control · Mathematics 2025-12-03 Juan José Maulén , Fernando Roldán , Cristian Vega

In this paper, we introduce a novel semidefinite programming framework for designing custom frugal resolvent splitting algorithms which find a zero in the sum of n monotone operators. This framework features a number of design choices which…

Optimization and Control · Mathematics 2024-09-04 Robert L Bassett , Peter Barkley