Tikhonov regularization of a second order dynamical system with Hessian driven damping

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the funct...

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Autores principales: Boţ, Radu Ioan, Csetnek, Ernö Robert, László, Szilárd Csaba
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Full Length Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550339/
https://www.ncbi.nlm.nih.gov/pubmed/34720194
http://dx.doi.org/10.1007/s10107-020-01528-8
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author Boţ, Radu Ioan
Csetnek, Ernö Robert
László, Szilárd Csaba
author_facet Boţ, Radu Ioan
Csetnek, Ernö Robert
László, Szilárd Csaba
author_sort Boţ, Radu Ioan
collection PubMed
description We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.
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spelling pubmed-85503392021-10-29 Tikhonov regularization of a second order dynamical system with Hessian driven damping Boţ, Radu Ioan Csetnek, Ernö Robert László, Szilárd Csaba Math Program Full Length Paper We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm. Springer Berlin Heidelberg 2020-06-11 2021 /pmc/articles/PMC8550339/ /pubmed/34720194 http://dx.doi.org/10.1007/s10107-020-01528-8 Text en © The Author(s) 2020 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 Full Length Paper
Boţ, Radu Ioan
Csetnek, Ernö Robert
László, Szilárd Csaba
Tikhonov regularization of a second order dynamical system with Hessian driven damping
title Tikhonov regularization of a second order dynamical system with Hessian driven damping
title_full Tikhonov regularization of a second order dynamical system with Hessian driven damping
title_fullStr Tikhonov regularization of a second order dynamical system with Hessian driven damping
title_full_unstemmed Tikhonov regularization of a second order dynamical system with Hessian driven damping
title_short Tikhonov regularization of a second order dynamical system with Hessian driven damping
title_sort tikhonov regularization of a second order dynamical system with hessian driven damping
topic Full Length Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550339/
https://www.ncbi.nlm.nih.gov/pubmed/34720194
http://dx.doi.org/10.1007/s10107-020-01528-8
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