# A minimum effort optimal control problem for elliptic PDEs

Christian Clason; Kazufumi Ito; Karl Kunisch

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

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topClason, 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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