On concepts of directional differentiability
type: Item
instance of: scholarly article
title: On concepts of directional differentiability
zbMATH Open document ID: 0682.49015
DOI: 10.1007/BF00940933
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of \(\sigma\)-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 4117307
zbMATH Keywords: sigma-directional differentiability
zbMATH Keywords: locally Lipschitz mappings
zbMATH Keywords: chain rule
author: Alexander Shapiro
reviewed by: Alexander Shapiro
Wikidata QID: Q61535192
MaRDI profile type: Publication
cites work: Q5534710
cites work: Q4194725
cites work: Q3884418
cites work: Optimization and nonsmooth analysis
cites work: An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems. I. General Theory
cites work: Various definitions of the derivative in mathematical programming
cites work: Introduction to sensitivity and stability analysis in nonlinear programming
cites work: Differential properties of the marginal function in mathematical programming
cites work: Directional differentiability of the optimal value function in a nonlinear programming problem
cites work: Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs
cites work: Stability in stochastic programming with recourse. Contaminated distributions
cites work: The theory of differentiation in linear topological spaces
cites work: The various definitions of the derivative in linear topological spaces
cites work: Q5645931
cites work: Differential calculus in topological linear spaces
cites work: Topology of mappings and differentiation processes
cites work: Q3237471
cites work: On locally-Lipschitz quasi-differentiate functions in Banach-spaces
cites work: Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
cites work: Q5558155
cites work: Conditions of differentiability in linear topological spaces
cites work: Q4767788
cites work: On quasidifferentiable mappings
description: scientific article; zbMATH DE number 4117307