\(L^\infty\)-stability of a parametric optimal control problem governed by semilinear elliptic equations
type: Item
instance of: scholarly article
title: \(L^\infty\)-stability of a parametric optimal control problem governed by semilinear elliptic equations
zbMATH Open document ID: 1475.49025
author: B. T. Kien
author: Nguyen Quoc Tuan
author: Ching-Feng Wen
author: Jen-Chih Yao
published in: Applied Mathematics and Optimization
publication date: 2021-08-11T00:00:00Z
review text: The paper studies the local \(L^\infty\)-stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. The present work expands on the results presented in [\textit{B. T. Kien} and \textit{J.-C. Yao}, ``Local stability of solutions to parametric semilinear elliptic optimal control problems'', Appl. Anal. Optim. 1, No. 3, 361--379 (2017)]. Under the assumption that that the zero-gap second-order optimality condition is satisfied, it is shown that the solution map is locally upper Hölder continuous at the reference parameter in the \(L^\infty\)-norm (and not only in the \(L^2\)-norm) of the control variable. First, the paper presents the key assumptions and the main theorem (local Hölder continuity in the \(L^\infty\)-norm; Theorem 2.1), followed by some auxiliary results. Subsequently, the authors present their main body of work -- the proof of Theorem 2.1.
reviewed by: Andreas Mang
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 7381023
zbMATH Keywords: solution stability
zbMATH Keywords: locally Hölder upper continuity
zbMATH Keywords: optimality condition
zbMATH Keywords: second-order sufficient optimality condition
MaRDI profile type: Publication
full work available at URL: s00245-020-09664-5
OpenAlex ID: W3010114761
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DOI: 10.1007/S00245-020-09664-5
description: scientific article; zbMATH DE number 7381023