Interior sphere condition for the graph of a multifunction
type: Item
instance of: scholarly article
title: Interior sphere condition for the graph of a multifunction
zbMATH Open document ID: 1312.49017
author: Chadi Nour
author: Jean Takche
published in: Set-Valued and Variational Analysis
publication date: 2014-09-18T00:00:00Z
review text: By introducing the notion of proximal-pseudo-differentiability for multifunctions, the authors prove the equivalence between the pointwise interior sphere condition of a multifunction and the interior sphere condition of its graph. This equivalence will open an ability for extending the semiconcavity results by \textit{C. Nour} and \textit{R. J. Stern} [Syst. Control Lett. 57, No. 10, 863--866 (2008; Zbl 1162.49021)] to the nonlinear case.
reviewed by: Do Van Luu
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 6345547
zbMATH Keywords: multifunctions
zbMATH Keywords: interior sphere condition
zbMATH Keywords: proximal-pseudo-differentiability
zbMATH Keywords: nonsmooth analysis
MaRDI profile type: Publication
full work available at URL: s11228-013-0268-x
OpenAlex ID: W2088941942
cites work: Convexity properties of the minimum time function
cites work: Semiconcave functions, Hamilton-Jacobi equations, and optimal control
cites work: Interior sphere property of attainable sets and time optimal control problems
cites work: Semiconcavity of the value function for exit time problems with nonsmooth target
cites work: Q4375488
cites work: Differentiability properties for a class of non-convex functions
cites work: Some New Regularity Properties for the Minimal Time Function
cites work: On the Structure of the Minimum Time Function
cites work: Hypographs satisfying an external sphere condition and the regularity of the minimum time function
cites work: Q3623523
cites work: Q3425531
cites work: Semiconcavity of the bilateral minimal time function: the linear case
cites work: The \(\theta \)-exterior sphere condition, \(\varphi \)-convexity, and local semiconcavity
cites work: Q2997140
cites work: On the union of closed balls property
cites work: Calculus Without Derivatives
cites work: Variational Analysis
DOI: 10.1007/S11228-013-0268-X
description: scientific article; zbMATH DE number 6345547