Paper Info
Title
Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints
Abstract
In this paper optimal control problems governed by the wave equation with control constraints are analyzed. Three types of control action are considered: distributed control, Neumann boundary control, and Dirichlet control, and proper functional analytic settings for them are discussed. For treating inequality constraints, semismooth Newton methods are discussed and their convergence properties are investigated. In the case of distributed and Neumann control, superlinear convergence is shown. For Dirichlet boundary control, superlinear convergence is proved for a strongly damped wave equation. For numerical realization, a space-time finite element discretization is discussed. Numerical examples illustrate the results.
Year
DOI
Venue
2011
10.1137/090766541
SIAM J. Control and Optimization
Keywords
Field
DocType
convergence property,control action,wave equation,neumann boundary control,control constraints,optimal control,semismooth newton methods,dirichlet boundary control,paper optimal control problem,neumann control,dirichlet control,superlinear convergence,space-time nite elements,control constraint,space time
Superlinear convergence,Convergence (routing),Discretization,Mathematical optimization,Optimal control,Mathematical analysis,Damped wave,Finite element method,Wave equation,Dirichlet distribution,Mathematics
Journal
Volume
Issue
ISSN
49
2
0363-0129
Citations 
PageRank 
References 
10
0.78
12
Authors
3
Name
Order
Citations
PageRank
Axel Kröner1214.60
Karl Kunisch21370145.58
Boris Vexler339740.49