Geodesic
Optimal control for one complex dynamic system,~II
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 3-18.

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The optimal control problem of the metal solidification in casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. A numerical algorithm for solving the direct problem was presented in the first part of this article, published in [1]. The optimal control problem was solved numerically using the gradient method. The gradient of the cost function was found with the help of conjugate problem. The discreet conjugate problem was posed with the help of Fast Automatic Differentiation technique. 
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Alla Albu; Vladimir Zubov. Optimal control for one complex dynamic system,~II. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 3-18. https://geodesic-test.mathdoc.fr/item/BASM_2009_2_a0/

[1] Albu A., Zubov V., “Optimal control for one complex dynamic system, I”, Bul. Acad. de Ştiinţe a Republicii Moldova Matematica, 2009, no. 1(59), 3–21 | MR | Zbl

[2] Evtushenko Y. G., “Computation of Exact Gradients in Distributed Dynamic Systems”, Optimizat. Methods and Software, 9 (1998), 45–75 | DOI | MR | Zbl

[3] Comp. Math. Math. Phys., 49:1 (2009), 47–70 | DOI | MR | MR | Zbl