Multiplier rules for Dini-derivatives in a topological vector space
Optimization and Control
2023-05-12 v1
Abstract
We provide new results of first-order necessary conditions of optimality problem in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. We establish our result in a topological vector space for problems with inequality constraints and in a Banach space for problems with equality and inequality constraints. Our contributions consist in the extension of the results known for the Fr\'echet and Gateaux-differentiable functions as well as for the Clarke's subdifferential of Lipschitz functions, to the more general Dini-differentiable functions. As consequences, we extend the result of B.H. Pourciau in \cite[Theorem 6, p. 445]{Po} from the convexity to the {\it "Dini-pseudoconvexity"}.
Cite
@article{arxiv.2305.06765,
title = {Multiplier rules for Dini-derivatives in a topological vector space},
author = {Mohammed Bachir and Rongzhen Lyu},
journal= {arXiv preprint arXiv:2305.06765},
year = {2023}
}