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In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method…

Optimization and Control · Mathematics 2025-11-07 Liqian Qin , Yuchao Tang , Jigen Peng

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

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

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

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…

Optimization and Control · Mathematics 2013-08-14 Dinh Dung , Bang Cong Vu

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

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 propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…

Optimization and Control · Mathematics 2016-04-08 R. Díaz Millán

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 present a new, stochastic variant of the projective splitting (PS) family of algorithms for monotone inclusion problems. It can solve min-max and noncooperative game formulations arising in applications such as robust ML without the…

Optimization and Control · Mathematics 2021-06-25 Patrick R. Johnstone , Jonathan Eckstein , Thomas Flynn , Shinjae Yoo

We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…

Functional Analysis · Mathematics 2014-07-02 Radu Ioan Bot , Ernö Robert Csetnek

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

We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent…

Optimization and Control · Mathematics 2024-03-18 Shida Wang , Jalal Fadili , Peter Ochs

In this paper, we propose two novel inertial-like algorithms for solving the split common null point problem (SCNPP) with respect to set-valued maximal operators. The features of the presented algorithm are using new inertial structure…

Numerical Analysis · Mathematics 2021-09-21 Yan Tang , Shiqing Zhang

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 paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

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 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

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan