Conservation law constrained optimization based upon Front-Tracking

Martin Gugat; Michaël Herty; Axel Klar; Gunter Leugering

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 40, Issue: 5, page 939-960
  • ISSN: 0764-583X

Abstract

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We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used in the numerical method called Front-Tracking.

How to cite

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Gugat, Martin, et al. "Conservation law constrained optimization based upon Front-Tracking." ESAIM: Mathematical Modelling and Numerical Analysis 40.5 (2007): 939-960. <http://eudml.org/doc/194342>.

@article{Gugat2007,
abstract = { We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used in the numerical method called Front-Tracking. },
author = {Gugat, Martin, Herty, Michaël, Klar, Axel, Leugering, Gunter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Sensitivity calculus; front-tracking; conservation laws.; conservation law; sensitivity analysis; Riemann problem; Front-Tracking; optimization},
language = {eng},
month = {1},
number = {5},
pages = {939-960},
publisher = {EDP Sciences},
title = {Conservation law constrained optimization based upon Front-Tracking},
url = {http://eudml.org/doc/194342},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Gugat, Martin
AU - Herty, Michaël
AU - Klar, Axel
AU - Leugering, Gunter
TI - Conservation law constrained optimization based upon Front-Tracking
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/1//
PB - EDP Sciences
VL - 40
IS - 5
SP - 939
EP - 960
AB - We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used in the numerical method called Front-Tracking.
LA - eng
KW - Sensitivity calculus; front-tracking; conservation laws.; conservation law; sensitivity analysis; Riemann problem; Front-Tracking; optimization
UR - http://eudml.org/doc/194342
ER -

References

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