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Inexact Proximal Newton methods in Hilbert spaces

Title data

Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Inexact Proximal Newton methods in Hilbert spaces.
In: Computational Optimization and Applications. (16 August 2023) . - pp. 1-37.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-023-00515-x

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Official URL: Volltext

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Project information

Project title:
Project's official title
Project's id
Nonsmooth Multi-Level Optimization Algorithms for Energetic Formulations of Finite-Strain Elastoplasticity
SCHI 1379/6-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We consider Proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global convergence and local acceleration of our method. The inexactness criteria are designed to be adequate for the Hilbert space framework we find ourselves in while traditional inexactness criteria from smooth Newton or finite dimensional Proximal Newton methods appear to be inefficient in this scenario. The performance of the method and its gain in effectiveness in contrast to the exact case are showcased considering a simple model problem in function space.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Nonlinear Optimization; Optimization in Hilbert space; Proximal Newton; Inexactness
Subject classification: Mathematics Subject Classification Code: 49M15 49M37 65K10
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Jul 2024 06:55
Last Modified: 02 Jul 2024 06:55
URI: https://eref.uni-bayreuth.de/id/eprint/89882

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