Newton Differentiability of Convex Functions in Normed Spaces and of a Class of Operators
Abstract
Newton differentiability is an important concept for analyzing generalized Newton methods for nonsmooth equations. In this work, for a convex function defined on an infinite-dimensional space, we discuss the relation between Newton and Bouligand differentiability and upper semicontinuity of its subdifferential. We also construct a Newton derivative of an operator of the form $(Fx)(p) = f(x,p)$ for general nonlinear operators $f$ that possess a Newton derivative with respect to $x$ and also for the case where $f$ is convex in $x$.
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Published In
DOI:10.1137/sjope8.32.2
Issue’s Table of Contents© 2022, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
Publication History
Published: 01 January 2022
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