A link between the steepest descent method and fixed-point iterations

We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler–Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the co...

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Detalles Bibliográficos
Autor principal: Heid, Pascal
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9813030/
https://www.ncbi.nlm.nih.gov/pubmed/36619368
http://dx.doi.org/10.1007/s11590-022-01867-9
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author Heid, Pascal
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description We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler–Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.
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spelling pubmed-98130302023-01-06 A link between the steepest descent method and fixed-point iterations Heid, Pascal Optim Lett Original Paper We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler–Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment. Springer Berlin Heidelberg 2022-03-18 2023 /pmc/articles/PMC9813030/ /pubmed/36619368 http://dx.doi.org/10.1007/s11590-022-01867-9 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Heid, Pascal
A link between the steepest descent method and fixed-point iterations
title A link between the steepest descent method and fixed-point iterations
title_full A link between the steepest descent method and fixed-point iterations
title_fullStr A link between the steepest descent method and fixed-point iterations
title_full_unstemmed A link between the steepest descent method and fixed-point iterations
title_short A link between the steepest descent method and fixed-point iterations
title_sort link between the steepest descent method and fixed-point iterations
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9813030/
https://www.ncbi.nlm.nih.gov/pubmed/36619368
http://dx.doi.org/10.1007/s11590-022-01867-9
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