English
Related papers

Related papers: Halpern-Type Accelerated and Splitting Algorithms …

200 papers

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

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is…

Optimization and Control · Mathematics 2021-07-22 Paul-Emile Maingé

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

In this paper, we propose and study the iteration complexity of an inexact Douglas-Rachford splitting (DRS) method and a Douglas-Rachford-Tseng's forward-backward (F-B) splitting method for solving two-operator and four-operator monotone…

Optimization and Control · Mathematics 2017-12-01 M. Marques Alves , M. Geremia

We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the…

Optimization and Control · Mathematics 2018-05-02 Hugo Raguet

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 consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

Optimization and Control · Mathematics 2015-11-17 Guoyin Li , Ting Kei Pong

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 develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…

Optimization and Control · Mathematics 2021-10-25 Vien V. Mai , Jacob Lindbäck , Mikael Johansson

The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well…

Optimization and Control · Mathematics 2020-04-14 Minh N. Dao , Hung M. Phan

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

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 consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock (2010) and Davis and Yin (2015) proposed accelerated…

Optimization and Control · Mathematics 2026-05-21 Govind M. Chari , Uijeong Jang , Ernest K. Ryu , Behçet Açıkmeşe

We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…

Optimization and Control · Mathematics 2023-04-21 Penghui Fu , Zhiqiang Tan

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…

Optimization and Control · Mathematics 2016-02-26 Lorenzo Rosasco , Silvia Villa , 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

In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth…

Optimization and Control · Mathematics 2024-04-24 Yonghong Yao , Lateef O. Jolaoso , Yekini Shehu , Jen-Chih Yao

In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed…

Optimization and Control · Mathematics 2021-09-22 Luis M. Briceño-Arias , Fernando Roldán