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In this article, we study two methods for solving monotone inclusions in real Hilbert spaces involving the sum of a maximally monotone operator, a monotone-Lipschitzian operator, a cocoercive operator, and a normal cone to a vector…

Optimization and Control · Mathematics 2024-05-13 Fernando Roldán

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 propose a variable metric extension of the forward--backward-forward algorithm for finding a zero of the sum of a maximally monotone operator and a Lipschitzian monotone operator in Hilbert spaces. In turn, this framework provides a…

Optimization and Control · Mathematics 2012-11-01 B. C. Vũ

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…

Optimization and Control · Mathematics 2010-11-29 L. Briceno-Arias , P. L. Combettes

We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…

Optimization and Control · Mathematics 2015-12-15 Radu Ioan Bot , Ernö Robert Csetnek

We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance…

Optimization and Control · Mathematics 2023-01-10 Xufeng Cai , Chaobing Song , Cristóbal Guzmán , Jelena Diakonikolas

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

A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous.…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Jonathan Eckstein

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…

Functional Analysis · Mathematics 2013-07-30 Radu Ioan Bot , Christopher Hendrich

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

We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…

Optimization and Control · Mathematics 2017-05-08 Radu Ioan Bot , Ernö Robert Csetnek

Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that the resolvents of the operators are available, this problem can be tackled with the…

Optimization and Control · Mathematics 2025-07-31 Heinz H. Bauschke , Shambhavi Singh , Xianfu Wang

In this paper we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another…

Functional Analysis · Mathematics 2014-07-02 Sebastian Banert , Radu Ioan Bot

The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…

Optimization and Control · Mathematics 2024-10-03 Olaniyi S. Iyiola , Lateef O. Jolaoso , Yekini Shehu

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

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 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

In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…

Optimization and Control · Mathematics 2024-10-30 Luis Briceño-Arias , Sergio López-Rivera , Emilio Vilches

In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

Optimization and Control · Mathematics 2020-06-17 Ernö Robert Csetnek , Yura Malitsky , Matthew K. Tam