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Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Optimization and Control · Mathematics 2019-10-29 Sulaiman A. Alghunaim , Kun Yuan , Ali H. Sayed

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…

Optimization and Control · Mathematics 2023-01-30 Dmitriy Metelev , Alexander Rogozin , Dmitry Kovalev , Alexander Gasnikov

We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…

Numerical Analysis · Mathematics 2026-03-11 Stephan Köhler , Oliver Rheinbach , Yue Xiang Tee , Sebastian Zug

A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing…

Numerical Analysis · Mathematics 2016-02-02 Y. Boubendir , H. Haddar , M. K. Riahi

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…

Numerical Analysis · Mathematics 2019-10-09 Jehanzeb Chaudhry , Don Estep , Simon Tavener

We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…

Optimization and Control · Mathematics 2026-05-11 Sen Na , Sungho Shin , Mihai Anitescu , Victor M. Zavala

In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…

Numerical Analysis · Mathematics 2019-10-21 Gabriele Ciaramella , Muhammad Hassan , Benjamin Stamm

In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave…

Numerical Analysis · Mathematics 2023-03-20 Nicolas Marsic , Christophe Geuzaine , Herbert De Gersem

In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…

Numerical Analysis · Mathematics 2024-02-13 Qiya Hu , Ziyi Li

We demonstrate that a small modification of the multiplicative, additive and restricted additive Schwarz preconditioner at the algebraic level, motivated by optimized Schwarz methods defined at the continuous level, leads to a significant…

Numerical Analysis · Mathematics 2007-05-23 Amik St-Cyr , Martin J. Gander , Stephen J. Thomas

A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational…

Numerical Analysis · Mathematics 2010-01-12 Michael Holst , Stefan Vandewalle

This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques…

Optimization and Control · Mathematics 2026-03-04 Xinliang Dai , Yuning Jiang , Yi Guo , Colin N. Jones , Moritz Diehl , Veit Hagenmeyer

Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method…

Numerical Analysis · Mathematics 2024-11-01 Alexander Heinlein , Kyrill Ho , Axel Klawonn , Martin Lanser

The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method, which has been…

Numerical Analysis · Mathematics 2022-06-14 Shihua Gong , Ivan G. Graham , Euan A. Spence

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…

Numerical Analysis · Mathematics 2016-11-03 Mingchao Cai , Luca F. Pavarino

Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…

Numerical Analysis · Mathematics 2026-05-26 Victorita Dolean , Pierre Jolivet , Frédéric Nataf , Pierre-Henri Tournier

Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive…

Signal Processing · Electrical Eng. & Systems 2023-03-01 Charles Hovine , Alexander Bertrand

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

Optimization and Control · Mathematics 2015-07-07 Nicholas Boyd , Geoffrey Schiebinger , Benjamin Recht

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…

Numerical Analysis · Mathematics 2019-12-20 Carlos Echeverría , Jörg Liesen , Petr Tichý

This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincar\'e operator and the…

Numerical Analysis · Mathematics 2013-12-30 Thi Thao Phuong Hoang , Jérôme Jaffré , Caroline Japhet , Michel Kern , Jean Roberts