Related papers: The Douglas-Rachford algorithm for two (not necess…
We consider distributed optimization in the client-server setting. By use of Douglas-Rachford splitting to the dual of the sum problem, we design a BFGS method that requires minimal communication (sending/receiving one vector per round for…
We present an efficient algorithm for regularized optimal transport. In contrast to previous methods, we use the Douglas-Rachford splitting technique to develop an efficient solver that can handle a broad class of regularizers. The…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…
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…
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…
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…
This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…
This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
We prove that the sequences generate by the Douglas-Rachford method converge weakly to a solution of the inclusion problem
In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM. When an optimization program is infeasible, unbounded, or pathological, the…
We propose the shadow Davis-Yin three-operator splitting method to solve nonconvex optimisation problems. Its convergence analysis is based on a merit function resembling the Moreau envelope. We explore variational analysis properties…
In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and…
The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods.…
We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…
In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…
Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…