Properties of projection and penalty methods for discretized elliptic control problems

Andrzej Cegielski; Christian Grossmann

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 1, page 23-41
  • ISSN: 1509-9407

Abstract

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In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.

How to cite

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Andrzej Cegielski, and Christian Grossmann. "Properties of projection and penalty methods for discretized elliptic control problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 23-41. <http://eudml.org/doc/271143>.

@article{AndrzejCegielski2007,
abstract = {In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.},
author = {Andrzej Cegielski, Christian Grossmann},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {convex programming; control of PDE; projection methods; penalty methods},
language = {eng},
number = {1},
pages = {23-41},
title = {Properties of projection and penalty methods for discretized elliptic control problems},
url = {http://eudml.org/doc/271143},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Andrzej Cegielski
AU - Christian Grossmann
TI - Properties of projection and penalty methods for discretized elliptic control problems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 1
SP - 23
EP - 41
AB - In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.
LA - eng
KW - convex programming; control of PDE; projection methods; penalty methods
UR - http://eudml.org/doc/271143
ER -

References

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  11. [11] A. Rösch, Error estimates for linear-quadratic control problems with control constraints, Optim. Methods Softw. 21 (2006), 121-134. Zbl1085.49042
  12. [12] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Theorie, Verfahren und Anwendungen, Vieweg, Wiesbaden 2005. 
  13. [13] M. Weiser, T. Gänzler and A. Schiela, A control reduced primal interior point method for PDE constrained optimization, ZIB Report 04-38, Zuse-Zentrum Berlin 2004. Zbl1190.90278
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