Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Second order semi-smooth Proximal Newton methods in Hilbert spaces

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006731
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

[img]
Format: PDF
Name: s10589-022-00369-9.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
Download (5MB)

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

Downloads

Downloads per month over past year