Stochastic augmented Lagrangian method in Riemannian shape manifolds

Geiersbach, Caroline; Suchan, Tim; Welker, Kathrin

doi:10.1007/s10957-024-02488-1

Stochastic augmented Lagrangian method in Riemannian shape manifolds

Publication date

2024-08-21

Document type

Forschungsartikel

Author

Geiersbach, Caroline

Suchan, Tim

Welker, Kathrin

Organisational unit

Mathematik im Bauingenieurwesen

DOI

10.1007/s10957-024-02488-1

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/22877

Publisher

Springer Science+Business Media

Series or journal

Journal of Optimization Theory and Applications

ISSN

0022-3239

Periodical volume

203

Periodical issue

1

First page

165

Last page

195

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Abstract

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.

Description

This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

Version

Published version

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