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A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…

Optimization and Control · Mathematics 2013-02-14 Patrick L. Combettes

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

Optimization and Control · Mathematics 2019-01-08 Hong-Kun Xu , Vera Roshchina

The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…

Numerical Analysis · Mathematics 2023-02-08 Hao Liu , Dong Wang

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…

Optimization and Control · Mathematics 2024-12-18 Farhana A. Simi , Matthew K. Tam

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…

Optimization and Control · Mathematics 2016-04-15 Meng Wen , Shigang Yue , Yuchao Tang , Jigen Peng

We propose a new class of primal-dual Fejer monotone algorithms for solving systems of com- posite monotone inclusions. Our construction is inspired by a framework used by Eckstein and Svaiter for the basic problem of finding a zero of the…

Optimization and Control · Mathematics 2014-10-07 Abdullah Alotaibi , Patrick L. Combettes , N. Shahzad

In this paper, we propose a distributed first-order algorithm with backtracking linesearch for solving multi-agent minimisation problems, where each agent handles a local objective involving nonsmooth and smooth components. Unlike existing…

Optimization and Control · Mathematics 2025-05-14 Felipe Atenas , Minh N. Dao , Matthew K. Tam

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

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…

Optimization and Control · Mathematics 2015-07-31 Damek Davis

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Machine Learning · Computer Science 2026-05-19 Mohammad S. Alkousa , Fedor S. Stonyakin , Belal A. Alashqar , Seydamet S. Ablaev

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…

Optimization and Control · Mathematics 2024-06-24 R. Díaz Millán , O. P. Ferreira , J. Ugon

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…

Functional Analysis · Mathematics 2013-07-30 Radu Ioan Bot , Christopher Hendrich

In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our…

Optimization and Control · Mathematics 2025-10-20 Radu Ioan Bot , Dang-Khoa Nguyen , Chunxiang Zong

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Optimization and Control · Mathematics 2012-06-29 Patrick L. Combettes , Bang C. Vũ

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…

Numerical Analysis · Mathematics 2022-10-12 Monika Eisenmann , Tony Stillfjord

We show that the asynchronous block-iterative primal-dual projective splitting framework introduced by P. L. Combettes and J. Eckstein in their 2018 Math. Program. paper can be viewed as an instantiation of the recently proposed warped…

Optimization and Control · Mathematics 2021-06-08 Minh N. Bùi

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao

The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…

Optimization and Control · Mathematics 2016-07-05 Pascal Bianchi , Walid Hachem