On solving elliptic obstacle problems by constant abs-linearization

Weiß, Olga; Weymuth, Monika

doi:10.1016/j.rico.2023.100309

On solving elliptic obstacle problems by constant abs-linearization

Publication date

2023-10-01

Document type

Forschungsartikel

Author

Weiß, Olga

Weymuth, Monika

Organisational unit

Mathematik

Institut für Mathematik und Computergestützte Simulation, UniBw M

DOI

10.1016/j.rico.2023.100309

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/22656

Publisher

Elsevier

Series or journal

Results in Control and Optimization

ISSN

2666-7207

Periodical volume

13

Article ID

100309

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Abstract

We consider optimal control problems governed by an elliptic variational inequality of the first kind, namely the obstacle problem. The variational inequality is treated by penalization, which leads to optimization problems governed by a nonsmooth semi-linear elliptic PDE. The CALi algorithm is then applied for the efficient solution of these nonsmooth optimization problems. The special feature of the optimization algorithm CALi is the treatment of the nonsmooth Lipschitz-continuous operators abs, max and min, which allows to explicitly exploit the nonsmooth structure. Stationary points are located by appropriate decomposition of the optimization problem into so-called smooth constant abs-linearized problems. Each of these constant abs-linearized problems can be solved by classical means. The comprehensive algorithmic concept is presented, and its performance is discussed through examples.

Description

This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Version

Published version

Access right on openHSU

Metadata only access