SEMISMOOTH NEWTON METHODS FOR OPTIMAL CONTROL OF THE WAVE EQUATION WITH CONTROL CONSTRAINTS

被引：42

作者：

Kroener, Axel ^{[1
]}

Kunisch, Karl ^{[2
]}

Vexler, Boris ^{[1
]}

机构：

[1] Tech Univ Munich, Fak Math, Lab Math Optimierung, D-85748 Garching, Germany

[2] Graz Univ, Inst Math & Sci Comp, A-8010 Graz, Austria

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 02期

基金：

奥地利科学基金会;

关键词：

semismooth Newton methods; wave equation; optimal control; control constraints; superlinear convergence; space-time finite elements; FINITE-ELEMENT METHODS; DIRICHLET BOUNDARY CONTROL; PARABOLIC OPTIMIZATION PROBLEMS; DOMAIN DECOMPOSITION; HYPERBOLIC-EQUATIONS; STATE CONSTRAINTS; TIME; SPACE; REGULARITY;

D O I：

10.1137/090766541

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：830 / 858

页数：29

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