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Recently, heuristics based on the Douglas-Rachford splitting algorithm and the alternating direction method of multipliers (ADMM) have found empirical success in minimizing convex functions over nonconvex sets, but not much has been done to…

Optimization and Control · Mathematics 2019-02-11 Shuvomoy Das Gupta

The basic optimization problem of road design is quite challenging due to a objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the…

Optimization and Control · Mathematics 2014-09-30 Heinz H. Bauschke , Valentin R. Koch , Hung M. Phan

The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility…

Optimization and Control · Mathematics 2020-04-14 Heinz H. Bauschke , Minh N. Dao , Dominikus Noll , Hung M. Phan

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…

Optimization and Control · Mathematics 2015-03-04 Pontus Giselsson

Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the…

Optimization and Control · Mathematics 2024-01-15 Regina S. Burachik , Bethany I. Caldwell , C. Yalçın Kaya

The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…

Optimization and Control · Mathematics 2025-11-07 Jan Harold Alcantara , Akiko Takeda

The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which…

Optimization and Control · Mathematics 2020-04-06 Minh N. Dao , Matthew K. Tam

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

Optimization and Control · Mathematics 2022-06-10 A. Benfenati , E. Chouzenoux , J. -C. Pesquet

The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two maximally monotone operators. Recent results concerned with…

Optimization and Control · Mathematics 2018-05-25 Walaa M. Moursi , Lieven Vandenberghe

We present the convergence analysis of convex combination of the alternating projection and Douglas-Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are…

Numerical Analysis · Mathematics 2020-02-06 Nguyen Hieu Thao , Oleg Soloviev , Michel Verhaegen

Douglas-Rachford method is a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Each of its iterations requires the sequential solution of two proximal subproblems. The aim of this work is to present a…

Optimization and Control · Mathematics 2018-09-10 Benar F. Svaiter

Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…

Numerical Analysis · Mathematics 2025-06-13 Liqi Guo , Ruike Xiang , Deren Han , Jiaxin Xie

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…

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

The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility…

Optimization and Control · Mathematics 2015-04-16 Heinz H. Bauschke , Walaa M. Moursi

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence.…

Optimization and Control · Mathematics 2020-04-14 Heinz H. Bauschke , Minh N. Dao

Learning from a stream of tasks usually pits plasticity against stability: acquiring new knowledge often causes catastrophic forgetting of past information. Most methods address this by summing competing loss terms, creating gradient…

Machine Learning · Computer Science 2026-05-20 Pourya Shamsolmoali , Masoumeh Zareapoor

The Douglas--Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being…

Optimization and Control · Mathematics 2020-04-14 Heinz H. Bauschke , Minh N. Dao , Scott B. Lindstrom

We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.

Optimization and Control · Mathematics 2015-07-01 Francisco J. Aragón Artacho , Jonathan M. Borwein , Matthew K. Tam

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions…

Optimization and Control · Mathematics 2018-04-04 Adil Salim , Pascal Bianchi , Walid Hachem

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…

Optimization and Control · Mathematics 2020-06-29 Wenqing Ouyang , Yue Peng , Yuxin Yao , Juyong Zhang , Bailin Deng