A necessary condition for the extremal problems under Gâteaux differentiability
type: Item
instance of: scholarly article
title: A necessary condition for the extremal problems under Gâteaux differentiability
zbMATH Open document ID: 0657.49011
DOI: 10.1016/0022-247X(88)90016-9
author: Urszula Ledzewicz
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The following so called smooth-convex optimization problem is considered: \(f_ 0(x,u)\to \inf\) subject to \(f_ i(x,u)\leq 0\), \(i=1,...,n\), \(F(x,u)=0\), \(u\in U\), where \(f_ i\) are functions on \(X\times U\), F: \(X\times U\to Y\) is an operator, U is a given subset of Y (X, Y are Banach spaces). The necessary local minimum condition is obtained under the following assumptions: \(f_ 0,f_ 1,...,f_ n\) are Fréchet-differentiable with respect to x and convex with respect to u, the operator F is Gâteaux- differentiable with respect to x and convex with respect to u. These assumptions are weaker than those assumed by \textit{A. D. Ioffe} and \textit{V. M. Tikhomirov} [Theory of extremal problems, (Russian) (1974; Zbl 0292.90042)].
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 49J50
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4073831
zbMATH Keywords: smooth-convex optimization
zbMATH Keywords: necessary local minimum condition
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
cites work: Contractor directions, directional contractors and directional contractions for solving equations
cites work: Q4138025
cites work: An application of the method of contractor directions to nonlinear programming
cites work: Application of the method of contractor directions to the Dubovitskii- Milyutin formalism
full work available at URL: 0022-247x(88)90016-9
OpenAlex ID: W2003558794
description: scientific article; zbMATH DE number 4073831