A minimum effort optimal control problem for elliptic PDEs

Christian Clason; Kazufumi Ito; Karl Kunisch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2012)

  • Volume: 46, Issue: 4, page 911-927
  • ISSN: 0764-583X

Abstract

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This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation illustrate the behavior of minimum effort controls.

How to cite

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Clason, Christian, Ito, Kazufumi, and Kunisch, Karl. "A minimum effort optimal control problem for elliptic PDEs." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.4 (2012): 911-927. <http://eudml.org/doc/273299>.

@article{Clason2012,
abstract = {This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation illustrate the behavior of minimum effort controls.},
author = {Clason, Christian, Ito, Kazufumi, Kunisch, Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {optimal control; minimum effort; L∞control cost; semi-smooth Newton method; control cost},
language = {eng},
number = {4},
pages = {911-927},
publisher = {EDP-Sciences},
title = {A minimum effort optimal control problem for elliptic PDEs},
url = {http://eudml.org/doc/273299},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Clason, Christian
AU - Ito, Kazufumi
AU - Kunisch, Karl
TI - A minimum effort optimal control problem for elliptic PDEs
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 4
SP - 911
EP - 927
AB - This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation illustrate the behavior of minimum effort controls.
LA - eng
KW - optimal control; minimum effort; L∞control cost; semi-smooth Newton method; control cost
UR - http://eudml.org/doc/273299
ER -

References

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