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Newton Differentiability of Convex Functions in Normed Spaces and of a Class of Operators

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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Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.32 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1265-1287

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SUBDIFFERENTIAL
CONVEX
SEMISMOOTH
NEWTON DERIVATIVE
BOULIGAND DERIVATIVE
MAXIMUM FUNCTIONAL
MEASURABLE SELECTOR

Info Detail Spesifik

https://doi.org/10.1137/21M1449531

Pernyataan Tanggungjawab

Martin Brokate, Michael Ulbrich

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