Suboptimal control over semilinear elliptic equations with phase constraints. II: Sensitivity, typicalness of the regular maximum principle
type: Item
instance of: scholarly article
title: Suboptimal control over semilinear elliptic equations with phase constraints. II: Sensitivity, typicalness of the regular maximum principle
zbMATH Open document ID: 1013.49011
author: M. I. Sumin
published in: Russian Mathematics
publication date: 2003-07-02T00:00:00Z
review text: The paper considers on optimal control problem governed by a semilinear elliptic equation with additional state constraints of the type \(y\in M+ q\subset C(Q)\), where \(Q\) is a compact subset of the reference domain \(\Omega\), \(M\) is a convex closed set with nonempty interior and \(q\) is a parameter. Necessary conditions which must satisfy approximating (with respect to the state constraints) minimizing sequences are given, and continuity properties (with respect to the parameter \(q\)) of the value of the problem are investigated. For Part I see [\textit{M. I. Sumin}, Russ. Math. 44, No. 6, 31-42 (2000); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2000, No. 6, 33-44 (2000; Zbl 1003.49020)].
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 1758688
zbMATH Keywords: necessary conditions for minimizing sequences
zbMATH Keywords: optimal control
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: state constraints
reviewed by: Uldis Raitums
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1758688