A minimum effort optimal control problem for elliptic PDEs
Christian Clason; Kazufumi Ito; Karl Kunisch
ESAIM: Mathematical Modelling and Numerical Analysis (2012)
- 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 46.4 (2012): 911-927. <http://eudml.org/doc/222120>.
@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},
keywords = {Optimal control; minimum effort; L∞control cost; semi-smooth Newton method; optimal control; control cost},
language = {eng},
month = {2},
number = {4},
pages = {911-927},
publisher = {EDP Sciences},
title = {A minimum effort optimal control problem for elliptic PDEs},
url = {http://eudml.org/doc/222120},
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
DA - 2012/2//
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; optimal control; control cost
UR - http://eudml.org/doc/222120
ER -
References
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