Multiplier rules for Dini-derivatives in a topological vector space

2023/05/11 by Bachir, Mohammed, Lyu, Rongzhen
#49K99 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 90C30 #Secondary 90C48

paper · doi:10.48550/arxiv.2305.06765

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 Fréchet 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".

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