Geodesic
An algorithm for solving the problem of boundary optimal control in a complex heat transfer model
Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 1, pp. 24-38

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A nonstationary model of complex heat transfer, which includes $P_1$ approximation for the radiative heat transfer equation, is considered. The optimal control problem consists in determination of the boundary reflection coefficient within the specified range in order to minimize the cost functional. The considered algorithm for solving the control problem is based on the fact, that the optimal control satisfies the bang-bang principle, and employs the idea of the gradient descent method. The algorithm is tested for a three-dimensional domain. 
@article{DVMG_2016_16_1_a2,
     author = {G. V. Grenkin},
     title = {An algorithm for solving the problem of boundary optimal control in a complex heat transfer model},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {24--38},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2016_16_1_a2/}
}
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G. V. Grenkin. An algorithm for solving the problem of boundary optimal control in a complex heat transfer model. Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 1, pp. 24-38. http://geodesic.mathdoc.fr/item/DVMG_2016_16_1_a2/