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Newton-type multilevel optimization method
File(s)
NeMo_pde_final.pdf (392.98 KB)
Accepted version
Author(s)
Ho, Chin Pang
Kocvara, Michal
Parpas, Panos
Type
Journal Article
Abstract
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models. The impressive performance of multilevel optimization methods is an empirical observation, and no theoretical explanation has so far been proposed. In order to address this issue, we study the convergence properties of a multilevel method that is motivated by second-order methods. We take the first step toward establishing how the structure of an optimization problem is related to the convergence rate of multilevel algorithms.
Date Issued
2022
Date Acceptance
2019-11-28
Citation
Optimization Methods and Software, 2022, 37 (1), pp.45-78
URI
URL
DOI
ISSN
1029-4937
Publisher
Taylor & Francis
Start Page
45
End Page
78
Journal / Book Title
Optimization Methods and Software
Volume
37
Issue
1
Copyright Statement
© 2019 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization Methods and Software on 13 December 2019, available online: https://doi.org/10.1080/10556788.2019.1700256
Sponsor
Engineering & Physical Science Research Council (E
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000502443800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/M028240/1
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
Newton's method
multilevel algorithms
multigrid methods
unconstrained optimization
ALGORITHM
Publication Status
Published
Date Publish Online
2019-12-13