ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - September 2006 - Volume 40, Issue 05  

Research Article

Conservation law constrained optimization based upon Front-Tracking

Gugat, Martina1, Herty, Michaëla2, Klar, Axela2 and Leugering, Guntera1

a1 Institut für Angewandte Mathematik, FAU Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany.

a2 Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.

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.

(Received November 15 2005)

(Online publication January 16 2007)

Key Words:

  • Sensitivity calculus;
  • front-tracking;
  • conservation laws.

Mathematics Subject Classification:

  • 35Lxx;
  • 76N15