Geodesic
On calculating of functional derivative for an optimal control problem
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 2, pp. 51-67

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The synthesis problem of a multilayer diffraction grating is formulated as an optimal control problem and consists in minimizing the cost functional depending on the geometric parameters of the grating profile. The gradient method is the most reliable and stable method for solving this problem. The paper deals with a method for calculating the gradient of the cost functional, which is done by solving a cojugate problem with special boundary conditions. Additionally, the paper discusses the numerical implementation of this solution and the calculation of the gradient. The results from a computational experiment are also presented.
Keywords: functional derivative, conjugate problem, optimal control problem, synthesis problem, diffraction gratings.
Mots-clés : gradient 
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     author = {M. O. Korpusov and M. V. Artemeva},
     title = {On calculating of functional derivative for an optimal control problem},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a4/}
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M. O. Korpusov; M. V. Artemeva. On calculating of functional derivative for an optimal control problem. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 2, pp. 51-67. http://geodesic.mathdoc.fr/item/VYURU_2024_17_2_a4/