Maximum principle for optimal control of non-well posed elliptic differential equations
type: Item
instance of: scholarly article
title: Maximum principle for optimal control of non-well posed elliptic differential equations
zbMATH Open document ID: 1032.49031
DOI: 10.1016/S0362-546X(01)00897-5
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The authors study optimal control problems governed by non-well-posed similinear elliptic differential equations. So the state equations are governed by nonmonotone operators and admit more than one solution. They ask to minimize the cost functional over all pairs \((y,u)\) where \(u\) is a control in the set of controls and \(y\) is a minimal positive solution of the state equation corresponding to \(u\). They introduce two kinds of new penalty functionals via which one can transform the original optimal control problem into optimization problems by thinking of the state equations as sets of constraints mixed by the state and the control. They use Ekeland's variational principle and some perturbation to obtain the necessary conditions for the solution of the optimization problem, then by passing to the limit they obtain the maximum principle for the original optimal control problem.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1880086
zbMATH Keywords: optimal control
zbMATH Keywords: non-well-posed equation
zbMATH Keywords: state constraint
zbMATH Keywords: similinear elliptic differential equations
zbMATH Keywords: Ekeland's variational principle
zbMATH Keywords: maximum principle
author: Gengsheng Wang
author: Lijuan Wang
reviewed by: Hussain A. El-Saify
MaRDI profile type: Publication
cites work: Q3694130
cites work: Analysis and control of nonlinear infinite dimensional systems
cites work: An Extension of Pontryagin’s Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities
cites work: Pontryagin's principle in the control of semilinear elliptic variational inequalities
cites work: Distributed control of systems governed by a general class of quasilinear elliptic equations
cites work: Optimal control of some semilinear elliptic equations with critical exponent
cites work: Necessary conditions for infinite-dimensional control problems
cites work: Necessary conditions for optimal control of elliptic systems
cites work: Q3331073
cites work: Necessary Conditions for Optimal Control of Distributed Parameter Systems
cites work: Optimal control of parabolic variational inequality involving state constraint
cites work: Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints
cites work: Q3472482
cites work: Neumann problems of semilinear elliptic equations involving critical Sobolev exponents
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description: scientific article; zbMATH DE number 1880086