Conservation law constrained optimization based upon front-tracking
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, p. 939-960

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.

DOI : https://doi.org/10.1051/m2an:2006037
Classification:  35Lxx,  76N15
Keywords: sensitivity calculus, front-tracking, conservation laws
@article{M2AN_2006__40_5_939_0,
     author = {Gugat, Martin and Herty, Micha\"el and Klar, Axel and Leugering, Gunter},
     title = {Conservation law constrained optimization based upon front-tracking},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {5},
     year = {2006},
     pages = {939-960},
     doi = {10.1051/m2an:2006037},
     zbl = {1116.65079},
     mrnumber = {2293253},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2006__40_5_939_0}
}
Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Gunter. Conservation law constrained optimization based upon front-tracking. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, pp. 939-960. doi : 10.1051/m2an:2006037. http://www.numdam.org/item/M2AN_2006__40_5_939_0/

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