Locally Lipschitz stability of solutions to a parametric parabolic optimal control problem with mixed pointwise constraints
type: Item
instance of: scholarly article
title: Locally Lipschitz stability of solutions to a parametric parabolic optimal control problem with mixed pointwise constraints
author: H. Khanh
published in: Applied Mathematics and Optimization
publication date: 2024-10-22T00:00:00Z
review text: Parametric optimal control is considered for semilinear parabolic boundary value problems with mixed inequality constraints. The parameters enter in the differential equation, the integral cost functional and the constraints. Under suitable regularity assumptions, if the strong second-order sufficient optimality condition is satisfied for given parameter, the solution is locally strong, and the optimal solutions (state and control) and corresponding Lagrange multipliers are locally Lipschitz continuous functions of the parameters. Sufficient conditions for the quadratic growth property of the cost functional are also proved.
reviewed by: Tullio Zolezzi
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 49K20
zbMATH DE Number: 7930232
zbMATH Keywords: solution stability
zbMATH Keywords: second-order sufficient optimality conditions
zbMATH Keywords: parametric parabolic control
zbMATH Keywords: mixed pointwise constraints
MaRDI profile type: Publication
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DOI: 10.1007/S00245-024-10191-W
description: scientific article; zbMATH DE number 7930232