Related papers: Convergence rates of Forward--Douglas--Rachford sp…
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…
In this work, we aim to establish the exact worst-case convergence rates of Douglas--Rachford splitting (DRS) and Davis--Yin splitting (DYS) when applied to convex optimization problems. Both DRS and DYS have two variants as swapping the…
We introduce and study a geometric modification of the Douglas-Rach\-ford method called the Circumcentered-Douglas-Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
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…
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,…
We develop two new algorithms, called, FedDR and asyncFedDR, for solving a fundamental nonconvex composite optimization problem in federated learning. Our algorithms rely on a novel combination between a nonconvex Douglas-Rachford splitting…
The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…
We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…
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…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
Although originally designed and analyzed for convex problems, the alternating direction method of multipliers (ADMM) and its close relatives, Douglas-Rachford splitting (DRS) and Peaceman-Rachford splitting (PRS), have been observed to…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…
Along with developing of Peaceman-Rachford Splittling Method (PRSM), many batch algorithms based on it have been studied very deeply. But almost no algorithm focused on the performance of stochastic version of PRSM. In this paper, we…
The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…