On \(G\)-semidifferentiable functions in Euclidean spaces
type: Item
instance of: scholarly article
title: On \(G\)-semidifferentiable functions in Euclidean spaces
zbMATH Open document ID: 0831.90108
DOI: 10.1007/BF02192233
author: Nguyen Dong Yen
published in: Journal of Optimization Theory and Applications
publication date: 1995-08-27T00:00:00Z
review text: We give a criterion for a function \(f: \mathbb{R}^n\to \mathbb{R}\) to be upper \(G\)-semidifferentiable in the sense of \textit{F. Gianessi} [ibid. 60, No. 2, 191-241 (1989; Zbl 0662.90071)] at a point \(\overline x\in \mathbb{R}^n\). Using this result, we describe upper \(G\)-semiderivatives when \(G\) is, for instance, one of the following basic classes of homogeneous functions: the set of all continuous positively homogeneous functions, the set of differences of two sublinear functions, and the set of sublinear functions. As a result, connections between upper \(G\)- semidifferentiability and the concepts of differentiability are obtained.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 790572
zbMATH Keywords: homogeneous functions
zbMATH Keywords: Dini-Hadamard directional derivatives
zbMATH Keywords: upper \(G\)- semidifferentiable
MaRDI profile type: Publication
cites work: Semidifferentiable functions and necessary optimality conditions
cites work: Sufficient conditions for extremum, penalty functions and regularity
cites work: Optimization and nonsmooth analysis
cites work: Abstract cone approximations and generalized differentiability in nonsmooth optimization
cites work: On semidifferentiable functions
cites work: Some notes on semidifferentiablity and generalized subdifferentials
cites work: Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
cites work: On a possible generalization of pshemchhy's quasidifferentiability
description: scientific article; zbMATH DE number 790572