Constructing a sequence of discrete Hessian matrices of an \(SC^{1}\) function uniformly convergent to the generalized Hessian matrix
type: Item
instance of: scholarly article
title: Constructing a sequence of discrete Hessian matrices of an \(SC^{1}\) function uniformly convergent to the generalized Hessian matrix
zbMATH Open document ID: 1198.49012
author: Rohollah Yousefpour
author: Nezam Mahdavi-Amiri
published in: Mathematical Programming. Series A. Series B
publication date: 2010-02-19T00:00:00Z
review text: For \(SC^{1}\) functions in the sense of \textit{J. S. Pang} and \textit{L. Qi} [J. Optimization Theory Appl. 85, 633--648 (1995; Zbl 0831.90095)], the authors introduce a notion of discrete Hessian matrix in such a way that the classical generalized Hessian matrix (i.e., Clarke's generalized Jacobian matrix of the gradient) coincides with the limit in the Hausdorff metric of a sequence of sets of discrete Hessian matrices.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C56
zbMATH DE Number: 5673355
zbMATH Keywords: discrete Hessian matrix
zbMATH Keywords: generalized Hessian matrix
zbMATH Keywords: semismooth function
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: s10107-008-0238-5
OpenAlex ID: W1991833659
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DOI: 10.1007/S10107-008-0238-5
description: scientific article; zbMATH DE number 5673355