Morozov's principle for the augmented Lagrangian method applied to linear inverse problems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.65103
DOI: 10.1137/100812835
author: Klaus Frick
author: Dirk A. Lorenz
author: Elena Resmerita
publication date: 2012-08-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.5181
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65J22
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 6064856
zbMATH Keywords: augmented Lagragian method
zbMATH Keywords: convex minimization problems
zbMATH Keywords: linear constraints
zbMATH Keywords: stopping rule
zbMATH Keywords: discrepancy principle
zbMATH Keywords: linear inverse problems
zbMATH Keywords: ill-posed optimization problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: iterative method
MaRDI profile type: Publication
OpenAlex ID: W3098416719
arXiv ID: 1010.5181
title: Morozov's principle for the augmented Lagrangian method applied to linear inverse problems
published in: Multiscale Modeling \& Simulation
review text: The paper deals with the ill-posed optimization problem \(J(u)\to \min\) subject to \(Ku=g\), where \(J:H_1 \to R\) is a convex functional and \(K:H_1 \to H_2\) is a linear bounded operator between Hilbert spaces \(H_1\) and \(H_2\). It is assumed that instead of exact data \(g \in H_2\) only noise-affected observation \(g^{\delta}\) is available, where \(\| g^{\delta}-g\| \leq \delta\). The authors study the iterative method \(u_n^{\delta} \in \text{{Argmin}}_{u \in H_1} (0.5 \tau_n \| Ku-g^{\delta}\|^2+ J(u)-\langle p_{n-1}^{\delta}, Ku-g^{\delta}\rangle)\),NEWLINENEWLINE \(p_n^{\delta}=p_{n-1}^{\delta}+\tau_n (g^{\delta}-Ku_n^{\delta})\); \(\tau_n>0\), with Morozov's discrepancy principle as a stopping rule.
reviewed by: Mikhail Yu. Kokurin
description: scientific article; zbMATH DE number 6064856