Lagrange Multipliers in locally convex spaces
Optimization and Control
2024-02-21 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2305.06736,
title = {Lagrange Multipliers in locally convex spaces},
author = {Mohammed Bachir and Joel Blot},
journal= {arXiv preprint arXiv:2305.06736},
year = {2024}
}