Legendre-type optimality conditions for a variational problem with inequality state constraints
type: Item
instance of: scholarly article
title: Legendre-type optimality conditions for a variational problem with inequality state constraints
zbMATH Open document ID: 0949.49015
author: Sayuri Koga
author: Hidefumi Kawasaki
published in: Mathematical Programming. Series A. Series B
publication date: 2000-07-21T00:00:00Z
review text: In optimization problems with infinitely many inequality constraints, the second-order necessary conditions usually contain an extra term which is due to the envelope effect discovered by the second author in 1988 [\textit{H. Kawasaki}, Math. Program., Ser. A 41, No. 1, 73--96 (1988; Zbl 0661.49012)]. In the theory of calculus of variations, the so-called state inequalities form an infinite system of inequalities. The main result of the paper states that, for such problems, the envelope effect does not appear in the Legendre condition, which is a second-order necessary condition for problems of the calculus of variations.
Mathematics Subject Classification ID: 49K05
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 1479740
zbMATH Keywords: Legendre condition
zbMATH Keywords: second-order optimality condition
zbMATH Keywords: envelope
zbMATH Keywords: inequality state constraint
zbMATH Keywords: weak minimal solution
reviewed by: Zsolt Páles
MaRDI profile type: Publication
full work available at URL: s101070050029
OpenAlex ID: W2026981187
DOI: 10.1007/S101070050029
description: scientific article; zbMATH DE number 1479740