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Second order semi-smooth proximal Newton methods in Hilbert spaces

Title data

Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Second order semi-smooth proximal Newton methods in Hilbert spaces.
Bayreuth , 2021 . - 28 p.

Official URL: Volltext

Project information

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

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering differentiability and convexity than in existing theory. As far as differentiability of the smooth part of the objective function is concerned, we introduce the notion of second order semi-smoothness and discuss why it constitutes an adequate framework for our Proximal Newton method. However, both global convergence as well as local acceleration still pertain to hold in our scenario. Eventually, the convergence properties of our algorithm are displayed by solving a toy model problem in function space.

Further data

Item Type: Preprint, postprint
Refereed: No
Keywords: Nonlinear Optimization; Proximal Newton; Second Order Semi-smoothness
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: 31 Mar 2021 09:29
Last Modified: 31 Mar 2021 09:29
URI: https://eref.uni-bayreuth.de/id/eprint/64523