Lagrange Multipliers in locally convex spaces

2023/05/11 by Bachir, Mohammed, Blot, Joel
#49J50 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Primary 46N10 #Secondary 46G05

paper · doi:10.48550/arxiv.2305.06736

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 \citeJa, 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.

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