Mean value theorem for functions possessing first order convex approximations. Applications in optimization theory
type: Item
instance of: scholarly article
title: Mean value theorem for functions possessing first order convex approximations. Applications in optimization theory
zbMATH Open document ID: 0572.58004
DOI: 10.4171/ZAA/142
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1985-01-01T00:00:00Z
review text: The main result of the paper is the following: Let X be an l.t.s., \(A\subset X\), [a,b]\(\subset int A\) and \(f: A\to R\) satisfying the conditions a) f is hemicontinuous on [a,b], b) for every \(x\in]a,b[\) there exists \(\phi_ x: X\to R\) a first order convex approximation for f at x and c) \(x\to \phi_ x(a-b)\), \(x\to \phi_ x(b-a)\) are upper semicontinuous. Then there exists \(c\in]a,b[\) and \(x^*\in \delta \phi_ c(0)\) such that \(f(b)-f(a)=<x^*,b-a>\). An application to optimization problems is given.
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 3913300
zbMATH Keywords: first order convex approximation
zbMATH Keywords: optimization problems
author: Marcin Studniarski
reviewed by: Constantin Zălinescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/142
OpenAlex ID: W2563655571
description: scientific article; zbMATH DE number 3913300