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Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…

Numerical Analysis · Mathematics 2015-06-10 Silvia Bonettini , Federica Porta , Valeria Ruggiero

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits…

Optimization and Control · Mathematics 2023-01-25 M. Marques Alves , Marina Geremia , Raul T. Marcavillaca

We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope…

Optimization and Control · Mathematics 2014-09-23 Panagiotis Patrinos , Lorenzo Stella , Alberto Bemporad

We consider an inertial primal-dual algorithm to compute 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…

Optimization and Control · Mathematics 2016-04-19 Meng Wen , Yu-Chao Tang , Jigen Peng

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…

Optimization and Control · Mathematics 2012-12-04 Radu Ioan Bot , Christopher Hendrich

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…

Optimization and Control · Mathematics 2020-06-03 Le Thi Khanh Hien , Nicolas Gillis , Panagiotis Patrinos

The classical Krasnoselskii-Mann iteration is broadly used for approximating fixed points of nonexpansive operators. To accelerate the convergence of the Krasnoselskii-Mann iteration, the inertial methods were received much attention in…

Functional Analysis · Mathematics 2020-01-09 Fuying Cui , Yang Yang , Yuchao Tang , Chuanxi Zhu

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…

Optimization and Control · Mathematics 2024-04-24 Yonghong Yao , Lateef O. Jolaoso , Yekini Shehu , Jen-Chih Yao

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

Optimization and Control · Mathematics 2015-07-06 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

We consider finite Markov decision processes (MDPs) with convex constraints and known dynamics. In principle, this problem is amenable to off-the-shelf convex optimization solvers, but typically this approach suffers from poor scalability.…

Optimization and Control · Mathematics 2024-12-19 Panagiotis D. Grontas , Anastasios Tsiamis , John Lygeros

We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding correctors corresponding to the…

Optimization and Control · Mathematics 2020-05-15 Tuomo Valkonen

In this paper, we study a parameterized Douglas-Rachford splitting method for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized…

Optimization and Control · Mathematics 2020-06-17 Fengmiao Bian , Xiaoqun Zhang

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…

Optimization and Control · Mathematics 2018-09-10 Benar F. Svaiter

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

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…

Optimization and Control · Mathematics 2022-06-16 Walaa M. Moursi

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…

Machine Learning · Computer Science 2025-05-08 İrfan Işik , Ibrahim Karahan , Okan Erkaymaz

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

Optimization and Control · Mathematics 2019-06-28 Jacob H. Seidman , Mahyar Fazlyab , Victor M. Preciado , George J. Pappas

In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…

Optimization and Control · Mathematics 2016-01-05 R. Díaz Millán

Three Operator Splitting (TOS) (Davis & Yin, 2017) can minimize the sum of multiple convex functions effectively when an efficient gradient oracle or proximal operator is available for each term. This requirement often fails in machine…

Optimization and Control · Mathematics 2022-02-21 Alp Yurtsever , Alex Gu , Suvrit Sra