## Title data

Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:

**Inexact Proximal Newton methods in Hilbert spaces.**

Bayreuth
,
2022
. - 27 p.

DOI: https://doi.org/10.48550/arXiv.2204.12168

## 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.