All-at-once preconditioning in PDE-constrained optimization

Tyrone Rees; Martin Stoll; Andy Wathen

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 341-360
  • ISSN: 0023-5954

Abstract

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The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques.

How to cite

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Rees, Tyrone, Stoll, Martin, and Wathen, Andy. "All-at-once preconditioning in PDE-constrained optimization." Kybernetika 46.2 (2010): 341-360. <http://eudml.org/doc/196697>.

@article{Rees2010,
abstract = {The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques.},
author = {Rees, Tyrone, Stoll, Martin, Wathen, Andy},
journal = {Kybernetika},
keywords = {optimal control; preconditioning; partial differential equations; partial differential equations; optimal control; preconditioning; saddle point problem; numerical results},
language = {eng},
number = {2},
pages = {341-360},
publisher = {Institute of Information Theory and Automation AS CR},
title = {All-at-once preconditioning in PDE-constrained optimization},
url = {http://eudml.org/doc/196697},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Rees, Tyrone
AU - Stoll, Martin
AU - Wathen, Andy
TI - All-at-once preconditioning in PDE-constrained optimization
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 341
EP - 360
AB - The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques.
LA - eng
KW - optimal control; preconditioning; partial differential equations; partial differential equations; optimal control; preconditioning; saddle point problem; numerical results
UR - http://eudml.org/doc/196697
ER -

References

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