Related papers: Adaptive Douglas-Rachford splitting algorithm for …
We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the…
In this work, we propose a new splitting algorithm for solving structured monotone inclusion problems composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. Our method…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…
This note is devoted to the splitting algorithm proposed by Davis and Yin in 2017 for computing a zero of the sum of three maximally monotone operators, with one of them being cocoercive. We provide a direct proof that guarantees its…
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…
In this paper, we propose the Bregman Douglas-Rachford splitting (BDRS) method and its variant Bregman Peaceman-Rachford splitting method for solving maximal monotone inclusion problem. We show that BDRS is equivalent to a Bregman…
The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…
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…
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…
We analyse the behaviour of the newly introduced cyclic Douglas-Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is…
Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and…