WIAS Preprint No. 3010, (2023)
Stochastic augmented Lagrangian method in shape spaces
Authors
- Geiersbach, Caroline
ORCID: 0000-0002-6518-7756 - Suchan, Tim
- Welker, Kathrin
2020 Mathematics Subject Classification
- 49Q10 60H35 35R15 49K20 41A25 60H15 60H30 35R60
Keywords
- augmented Lagrangian, stochastic optimization, uncertainties, inequality constraints, Riemannian manifold, shape optimization, geometric constraints
DOI
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.
Appeared in
- J. Optim. Theory Appl., published online on 21.08.2024, DOI 10.1007/s10957-024-02488-1 under the title ``Stochastic augmented Lagrangian method in Riemannian shape manifolds."
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