First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929251184279552 |
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| author | Bergmann, Ronny Herzog, Roland López, Julián Ortiz Schiela, Anton |
| author_facet | Bergmann, Ronny Herzog, Roland López, Julián Ortiz Schiela, Anton |
| contents | We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the feasible set as the preimage of a submanifold with corners of the codomain. The latter is a subset which corresponds to a convex cone locally in suitable charts. We study first- and second-order optimality conditions for this class of problems. We also show the invariance of the relevant quantities with respect to local representations of the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_04882 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints Bergmann, Ronny Herzog, Roland López, Julián Ortiz Schiela, Anton Optimization and Control We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the feasible set as the preimage of a submanifold with corners of the codomain. The latter is a subset which corresponds to a convex cone locally in suitable charts. We study first- and second-order optimality conditions for this class of problems. We also show the invariance of the relevant quantities with respect to local representations of the problem. |
| title | First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2110.04882 |