Maximum principle for state-constrained control of some semilinear parabolic differential equations
type: Item
instance of: scholarly article
title: Maximum principle for state-constrained control of some semilinear parabolic differential equations
zbMATH Open document ID: 1032.49030
DOI: 10.1023/A:1019685231733
author: C. Liu
author: Gengsheng Wang
published in: Journal of Optimization Theory and Applications
publication date: 2003-06-09T00:00:00Z
review text: The authors study the optimal control problem for some semilinear parabolic differential equations, having a local solution only, which may be governed by nonmonotone operators. They transform the original optimal control problems into optimization problems of state and control variables by considering the state equations as mixed constraints involving the above two variables. The controls enter the state systems nonlinearity, so they define new penalty functionals which transform the original optimal control problems into optimization problems which approximate original problems. Then by Ekeland's variational principle they obtain the optimal solution. Finally, they pass to the limit to obtain the maximum principle for the original optimal control problem.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 1924989
zbMATH Keywords: optimal control
zbMATH Keywords: non-well-posed equations
zbMATH Keywords: maximum principle
zbMATH Keywords: state constraints
zbMATH Keywords: semilinear parabolic differential equations
zbMATH Keywords: mixed constraints
zbMATH Keywords: Ekeland's variational principle
reviewed by: Hussain A. El-Saify
MaRDI profile type: Publication
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full work available at URL: a:1019685231733
OpenAlex ID: W1501178829
description: scientific article; zbMATH DE number 1924989