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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.07451 |
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| _version_ | 1866912319495208960 |
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| author | Westerhout, Jacob Guo, Xin Nguyen, Hien Duy |
| author_facet | Westerhout, Jacob Guo, Xin Nguyen, Hien Duy |
| contents | Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity conditions that enable more general theorem statements. In the context of unstructured optimization over topological domains, we collect these continuity conditions from disparate sources and review their applications. As primary outcomes, we prove two comprehensive implication diagrams that establish novel connections between the reviewed conditions. In doing so, we also introduce previously missing continuity conditions and provide new counterexamples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuity conditions weaker than lower semi-continuity Westerhout, Jacob Guo, Xin Nguyen, Hien Duy Optimization and Control Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity conditions that enable more general theorem statements. In the context of unstructured optimization over topological domains, we collect these continuity conditions from disparate sources and review their applications. As primary outcomes, we prove two comprehensive implication diagrams that establish novel connections between the reviewed conditions. In doing so, we also introduce previously missing continuity conditions and provide new counterexamples. |
| title | Continuity conditions weaker than lower semi-continuity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.07451 |