Quasidifferentiability of real-valued functions and local extremum conditions
type: Item
instance of: scholarly article
title: Quasidifferentiability of real-valued functions and local extremum conditions
zbMATH Open document ID: 0569.49005
DOI: 10.1007/BF00968978
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: For real-valued functions defined on a finite-dimensional Euclidean space, we introduce the concepts of \(\epsilon\)-quasidifferentials (lower and upper) and quasidifferentiability (lower, upper). The class of functions having the property of quasidifferentiability in the sense of the present paper is sufficiently broad. We note that any locally Lipschitz function is lower and upper quasidifferentiable. The fundamental formulas of the calculus of \(\epsilon\)-quasidifferentials are given. For functions having lower (upper) \(\epsilon\)-quasidifferential, we establish both necessary and also sufficient conditions for a local minimum (maximum). We show that for a wide class of functions, necessary and also sufficient conditions for a local minimum (maximum) can be formulated in terms of quasidifferentiable lower (upper) local approximations.
Mathematics Subject Classification ID: 49J50
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3909180
zbMATH Keywords: \(\epsilon \) -quasidifferentials
zbMATH Keywords: quasidifferentiability
zbMATH Keywords: local minimum
author: V. V. Gorokhovik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3909180