English
Related papers

Related papers: Primal-dual splitting for structured composite mon…

200 papers

In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…

Optimization and Control · Mathematics 2014-03-26 Boushra Abbas , Hedy Attouch

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…

Optimization and Control · Mathematics 2012-02-14 Thomas L. Magnanti , Dan Stratila

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

Optimization and Control · Mathematics 2021-10-29 Quoc Tran-Dinh , Deyi Liu

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

Optimization and Control · Mathematics 2021-03-17 Nguyen Van Dung , Băng Công Vũ

We tackle highly nonconvex, nonsmooth composite optimization problems whose objectives comprise a Moreau-Yosida regularized term. Classical nonconvex proximal splitting algorithms, such as nonconvex ADMM, suffer from lack of convergence for…

Optimization and Control · Mathematics 2018-02-28 Emanuel Laude , Tao Wu , Daniel Cremers

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm

In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…

Optimization and Control · Mathematics 2022-03-02 Rubén Campoy

In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

Optimization and Control · Mathematics 2020-06-17 Ernö Robert Csetnek , Yura Malitsky , Matthew K. Tam

We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…

Optimization and Control · Mathematics 2024-11-20 Patrick L. Combettes

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…

Optimization and Control · Mathematics 2021-06-30 Xin He , Rong Hu , Ya-Ping Fang

This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…

Optimization and Control · Mathematics 2024-08-30 Olivier Bilenne

Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators…

Optimization and Control · Mathematics 2021-04-13 Minh N. Dao , Hung M. Phan

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…

Optimization and Control · Mathematics 2025-10-03 Anshika Anshika , Jiaxing Li , Debdas Ghosh , Xiangxiong Zhang

In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the…

Optimization and Control · Mathematics 2020-08-31 Bing Tan , Zheng Zhou , Xiaolong Qin

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…

Optimization and Control · Mathematics 2024-08-28 Yu Gao , Xiaochuan Pan , Chong Chen

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…

Optimization and Control · Mathematics 2022-07-15 Luis Briceño-Arias , Nelly Pustelnik

In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators. Our method converges under the same assumptions as Tseng's forward-backward-forward method,…

Optimization and Control · Mathematics 2020-05-08 Yura Malitsky , Matthew K. Tam

We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a…

Optimization and Control · Mathematics 2020-09-25 Stanislav Mazurenko , Jyrki Jauhiainen , Tuomo Valkonen

In this paper, a centralized two-block separable optimization is considered for which a fully parallel primal-dual discrete-time algorithm with fixed step size is derived based on monotone operator splitting method. In this algorithm, the…

Optimization and Control · Mathematics 2020-09-30 S. Sh. Alaviani , A. G. Kelkar

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

Optimization and Control · Mathematics 2017-10-09 Junyu Zhang , Shiqian Ma , Shuzhong Zhang