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Lagrange Multipliers in locally convex spaces - MaRDI portal

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Lagrange Multipliers in locally convex spaces

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Publication:6510061

arXiv2305.06736MaRDI QIDQ6510061

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Abstract: 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 Fr'echet-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.





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