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URN to cite this document: urn:nbn:de:bvb:703-epub-6731-2
Title data
Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Second order semi-smooth Proximal Newton methods in Hilbert spaces.
In: Computational Optimization and Applications.
Vol. 82
(2022)
Issue 2
.
- pp. 465-498.
ISSN 1573-2894
DOI der Verlagsversion: https://doi.org/10.1007/s10589-022-00369-9
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Abstract
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: | Article in a journal |
|---|---|
| Keywords: | Non-smooth Optimization; Optimization in Hilbert space; Proximal Newton |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela 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 Applied Mathematics |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-6731-2 |
| Date Deposited: | 27 Oct 2022 09:25 |
| Last Modified: | 27 Oct 2022 09:25 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/6731 |
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