Geodesic
Functional gradient evaluation in the optimal control of a complex dynamical system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 814-833 
A. V. Albu; A. F. Albu; V. I. Zubov. Functional gradient evaluation in the optimal control of a complex dynamical system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 814-833. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a6/
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     title = {Functional gradient evaluation in the optimal control of a~complex dynamical system},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The gradient of the cost functional in a discrete optimal control problem for metal solidification in metal casting is exactly calculated. In contrast to previous studies, the object under analysis has a complex geometric shape. The mathematical model for describing the solidification process is based on a three-dimensional two-phase initial–boundary value problem of the Stefan type. Formulas for exact gradient evaluation are derived using the fast automatic differentiation technique.

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[2] Albu A. F., Zubov V. I., “Vychislenie gradienta funktsionala v odnoi zadache optimalnogo upravleniya, svyazannoi s kristallizatsiei metalla”, Zh. vychisl. matem. i matem. fiz., 49:1 (2009), 51–75

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[5] Albu A. F., Zubov V. I., “O vybore funktsionala i raznostnoi skhemy pri reshenii zadachi optimalnogo upravleniya protsessom kristallizatsii metalla”, Zh. vychisl. matem. i matem. fiz., 51:1 (2011), 24–38

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