Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913767162380288 |
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| author | Geiersbach, Caroline Suchan, Tim Welker, Kathrin |
| author_facet | Geiersbach, Caroline Suchan, Tim Welker, Kathrin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_17404 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds Geiersbach, Caroline Suchan, Tim Welker, Kathrin Optimization and Control 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. |
| title | Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2303.17404 |