Discretization of nonlinear elliptic optimal control problems
type: Item
instance of: scholarly article
title: Discretization of nonlinear elliptic optimal control problems
zbMATH Open document ID: 0806.49023
DOI: 10.1016/0167-6911(94)90017-5
author: I. Chryssoverghi
author: Basilis Kokkinis
published in: Systems \& Control Letters
publication date: 1995-02-16T00:00:00Z
review text: The authors consider a state-constrained optimal control problem for systems defined by semilinear elliptic partial differential equations. The relaxation theory, as presented by \textit{J. Warga} [Optimal control of differential and functional equations (1972; Zbl 0253.49001)], is applied to the study of the control problem. The main concern of the paper is the analysis of the numerical approximations. By using finite element methods, they discretize the control problem and prove that the limit points of the sequences of discrete optimal controls are solutions of the continuous relaxed problem.
Mathematics Subject Classification ID: 49M20
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 550133
zbMATH Keywords: semilinear elliptic partial differential equations
zbMATH Keywords: relaxation theory
zbMATH Keywords: discrete optimal controls
reviewed by: Eduardo Casas
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90017-5
OpenAlex ID: W1965145250
cites work: Numerical approximation of nonconvex optimal control problems defined by parabolic equations
cites work: Nonconvex optimal control of nonlinear monotone parabolic systems
cites work: Discrete approximation of relaxed optimal control problems
cites work: Approximation of relaxed nonlinear parabolic optimal control problems
cites work: An explicit procedure for discretizing continuous, optimal control problems
cites work: Sur le contrôle optimal de systèmes gouvernés par des équations élliptiques. (On optimal control of systems gouverned by elliptic equations.)
cites work: Q5890172
cites work: A computational method for a class of optimal relaxed control problems
cites work: Q5667133
cites work: Steepest Descent with Relaxed Controls
cites work: Relaxed Controls and the Convergence of Optimal Control Algorithms
description: scientific article; zbMATH DE number 550133