Geodesic
Optimal control for one complex dynamic system,~I
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 3-21

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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 is presented for solving the direct problem. 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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     author = {Alla Albu and Vladimir Zubov},
     title = {Optimal control for one complex dynamic {system,~I}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--21},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/BASM_2009_1_a0/}
}
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Alla Albu; Vladimir Zubov. Optimal control for one complex dynamic system,~I. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 3-21. http://geodesic.mathdoc.fr/item/BASM_2009_1_a0/