Clarke's tangent vectors as tangents to Lipschitz continuous curves
type: Item
instance of: scholarly article
title: Clarke's tangent vectors as tangents to Lipschitz continuous curves
zbMATH Open document ID: 0535.90073
DOI: 10.1007/BF00939984
author: G. G. Watkins
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: Each Clarke tangent vector to a closed set in \({\mathbb{R}}^ n\) at a point in the set is shown to be strictly tangent at that point to some Lipschitz continuous curve lying in the set. This result is quite different in nature from current descriptions of the Clarke tangent cone due to Clarke, Hiriart-Urruty, and others. For the case where the Clarke tangent cone is solid, it is shown that most of the tangential approximants in use in the literature coincide.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3850832
zbMATH Keywords: contingent cone
zbMATH Keywords: Lipschitz continuous maps
zbMATH Keywords: strict differentiability
zbMATH Keywords: tent
zbMATH Keywords: Clarke tangent vector
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939984
OpenAlex ID: W1969325112
description: scientific article; zbMATH DE number 3850832