Approximating Clarke's subgradients of semismooth functions by divided differences
type: Item
instance of: scholarly article
title: Approximating Clarke's subgradients of semismooth functions by divided differences
zbMATH Open document ID: 1133.65043
author: Rahmo El-Desouky
author: Marcin Studniarski
published in: Numerical Algorithms
publication date: 2007-04-19T00:00:00Z
review text: The aim of this paper is to demonstrate that the algorithm proposed by \textit{M. Studniarski} [Numer. Math. 55, 685--693 (1989; Zbl 0671.65044)] can be extended to a more general class of nonsmooth functions. That class is the one of semismooth functions introduced by \textit{R. Mifflin} [SIAM J. Control Optim. 15, 959--972 (1977; Zbl 0376.90081)]. A semismooth function has generalized gradients in the sense of Clarke and one-sided directional derivatives in every direction. The algorithm in the present paper works only for functions of two variables. Its convergence is demonstrated and some numerical tests are presented.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5145106
zbMATH Keywords: semismooth functions
zbMATH Keywords: Clarke's subgradients
zbMATH Keywords: numerical examples
zbMATH Keywords: nondifferentiable functions
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
full work available at URL: s11075-007-9069-3
OpenAlex ID: W1982706353
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DOI: 10.1007/S11075-007-9069-3
description: scientific article; zbMATH DE number 5145106