Related papers: A distributed Douglas-Rachford splitting method fo…
In this work we address the problem of distributed optimization of the sum of convex cost functions in the context of multi-agent systems over lossy communication networks. Building upon operator theory, first, we derive an ADMM-like…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
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,…
Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its…
We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…
Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval. Fixed point analysis shows that the DRS iterated…
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
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…
More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas-Rachford algorithm. Today, this method is well recognized as a classical and highly successful splitting method to find minimizers of the sum of two (not…
Our interest lies in developing some efficient methods for minimizing the sum of two geodesically convex functions on Hadamard manifolds, with the aim to enhance the convergence of the Douglas-Rachford algorithm in Hadamard manifolds.…
The Douglas-Rachford algorithm is one of the most prominent splitting algorithms for solving convex optimization problems. Recently, the method has been successful in finding a generalized solution (provided that one exists) for…
This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a…
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…
We consider the problem of non-smooth convex optimization with linear equality constraints, where the objective function is only accessible through its proximal operator. This problem arises in many different fields such as statistical…
The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to…
In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into…
We examine convergence properties of continuous-time variants of accelerated Forward-Backward (FB) and Douglas-Rachford (DR) splitting algorithms for nonsmooth composite optimization problems. When the objective function is given by the sum…
We consider the problem of minimizing the sum of a convex function and a convex function composed with an injective linear mapping. For such problems, subject to a coercivity condition at fixed points of the corresponding Picard iteration,…