No-gap second-order conditions for minimization problems in spaces of measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916164114841600 |
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| author | Wachsmuth, Gerd Walter, Daniel |
| author_facet | Wachsmuth, Gerd Walter, Daniel |
| contents | Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical analysis is played by the assumption that the optimal dual state admits finitely many global extrema and satisfies a second-order sufficient optimality condition in each one of them. In this work, we show the full equivalence of these structural assumptions to a no-gap second-order condition involving the second subderivative of the Radon norm as well as to a local quadratic growth property of the objective functional with respect to the bounded Lipschitz norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No-gap second-order conditions for minimization problems in spaces of measures Wachsmuth, Gerd Walter, Daniel Optimization and Control 46E27, 49K27, 49J52, 49J53 Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical analysis is played by the assumption that the optimal dual state admits finitely many global extrema and satisfies a second-order sufficient optimality condition in each one of them. In this work, we show the full equivalence of these structural assumptions to a no-gap second-order condition involving the second subderivative of the Radon norm as well as to a local quadratic growth property of the objective functional with respect to the bounded Lipschitz norm. |
| title | No-gap second-order conditions for minimization problems in spaces of measures |
| topic | Optimization and Control 46E27, 49K27, 49J52, 49J53 |
| url | https://arxiv.org/abs/2403.12001 |