Optimal control of parabolic problems with state constraints: A penalization method for optimality conditions
type: Item
instance of: scholarly article
title: Optimal control of parabolic problems with state constraints: A penalization method for optimality conditions
zbMATH Open document ID: 0813.49024
DOI: 10.1007/BF01189479
published in: Applied Mathematics and Optimization
publication date: 1995-06-11T00:00:00Z
review text: The author studies state constrained optimal control problems with parabolic evolution equations. Optimality conditions are derived where the state and control expressions have been decoupled. The approach used is to consider a family of problems where deviation of the dynamics from feasibility is penalized through a parameter \(\varepsilon\). Decoupled optimality conditions are determined for each of these problems. Using Slater-like assumptions the limit of these optimality conditions provide optimality conditions for the original problem and the existence of Lagrange multipliers. The method is demonstrated on a distributed control problem with a Dirichlet boundary condition, and a boundary control problem with a Neumann boundary condition.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 563450
zbMATH Keywords: optimal control
zbMATH Keywords: parabolic evolution equations
zbMATH Keywords: optimality conditions
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: Neumann boundary condition
author: M. Bergounioux
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189479
OpenAlex ID: W1551245337
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description: scientific article; zbMATH DE number 563450