## 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)
.
- pp. 465-498.

ISSN 0926-6003

DOI: https://doi.org/10.1007/s10589-022-00369-9

## 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 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.