Slater conditions without interior points for programs in Lebesgue spaces with pointwise bounds and finitely many constraints
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909126206947328 |
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| author | Wachsmuth, Gerd |
| author_facet | Wachsmuth, Gerd |
| contents | We consider optimization problems in Lebesgue spaces with pointwise box constraints and finitely many additional linear constraints. We prove that the existence of a Slater point which lies strictly between the pointwise bounds and which satisfies the linear constraints is sufficient for the existence of Lagrange multipliers. Surprisingly, the Slater point is also necessary for the existence of Lagrange multipliers in a certain sense. We also demonstrate how to handle additional finitely many nonlinear constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11249 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Slater conditions without interior points for programs in Lebesgue spaces with pointwise bounds and finitely many constraints Wachsmuth, Gerd Optimization and Control 49K27, 90C46 We consider optimization problems in Lebesgue spaces with pointwise box constraints and finitely many additional linear constraints. We prove that the existence of a Slater point which lies strictly between the pointwise bounds and which satisfies the linear constraints is sufficient for the existence of Lagrange multipliers. Surprisingly, the Slater point is also necessary for the existence of Lagrange multipliers in a certain sense. We also demonstrate how to handle additional finitely many nonlinear constraints. |
| title | Slater conditions without interior points for programs in Lebesgue spaces with pointwise bounds and finitely many constraints |
| topic | Optimization and Control 49K27, 90C46 |
| url | https://arxiv.org/abs/2212.11249 |