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GÂteaux-Differentiability of Convex Functions in Infinite Dimension

2018/02/21 by Mohammed Bachir, Bachir, Mohammed, Adrien Fabre +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1802.07633

arxiv created 2018/02/21 · arxiv updated 2018/02/22

Abstract

It is well known that in Rn , Gâteaux (hence Fréchet) differ-entiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point. We prove that this result extends naturally to certain infinite dimensional vector spaces, in particular to Banach spaces having a Schauder basis.

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