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Conservation law constrained optimization based upon Front-Tracking

Published online by Cambridge University Press:  16 January 2007

Martin Gugat ,
Michaël Herty ,
Axel Klar  and
Gunter Leugering
Martin Gugat
Affiliation:
Institut für Angewandte Mathematik, FAU Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany.
Michaël Herty
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.
Axel Klar
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.
Gunter Leugering
Affiliation:
Institut für Angewandte Mathematik, FAU Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany.
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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.

Keywords

Sensitivity calculusfront-trackingconservation laws.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 5 , September 2006 , pp. 939 - 960
Copyright
© EDP Sciences, SMAI, 2007

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