Lagrange Multipliers in locally convex spaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914685276651520 |
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| author | Bachir, Mohammed Blot, Joel |
| author_facet | Bachir, Mohammed Blot, Joel |
| contents | We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of J. Jahn in \cite{Ja}, replacing Fréchet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called {\it ``admissible sets"}. Examples illustrating our results are given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_06736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lagrange Multipliers in locally convex spaces Bachir, Mohammed Blot, Joel Optimization and Control Functional Analysis Primary 46N10, 49J50, Secondary 46G05 We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of J. Jahn in \cite{Ja}, replacing Fréchet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called {\it ``admissible sets"}. Examples illustrating our results are given. |
| title | Lagrange Multipliers in locally convex spaces |
| topic | Optimization and Control Functional Analysis Primary 46N10, 49J50, Secondary 46G05 |
| url | https://arxiv.org/abs/2305.06736 |