Gâteaux semiderivative approach applied to shape optimization of obstacle problems

Goldammer, Nico; Schulz, Volker H.; Welker, Kathrin

doi:10.2478/candc-2024-0007

Gâteaux semiderivative approach applied to shape optimization of obstacle problems

Publication date

2025-01-17

Document type

Forschungsartikel

Author

Goldammer, Nico

Schulz, Volker H.

Welker, Kathrin

Organisational unit

Mathematik

Mathematik im Bauingenieurwesen

DOI

10.2478/candc-2024-0007

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/22977

Publisher

Systems Research Institute, Polish Academy of Sciences (SRI PAS)

Series or journal

Control and Cybernetics

ISSN

0324-8569

Periodical volume

53

Periodical issue

1

First page

141

Last page

161

Part of the university bibliography

✅

Language

English

Abstract

Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs, as well as distributed, non-linear, non-convex and infinite-dimensional aspects, due to the shapes, which complicate setting up an optimality system and, thus, developing efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives for the purpose of formulating optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the obstacle problem.

Description

License: CC BY-NC-ND 4.0 (https://creativecommons.org/licenses/by-nc-nd/4.0)

Version

Published version

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