The paper is devoted to the optimization of a first mixed initial-boundary value problem for hyperbolic differential inclusions (DFIs) with Laplace operator. For this, an auxiliary problem with a hyperbolic discrete inclusion is defined and, using locally conjugate mappings, necessary and sufficient optimality conditions for hyperbolic discrete inclusions are proved. Then, using the method of discretization of hyperbolic DFIs and the already obtained optimality conditions for discrete inclusions, the optimality conditions for the discrete approximate problem are formulated in the form of the Euler-Lagrange type inclusion. Thus, using specially proved equivalence theorems, which are the only tool for constructing Euler-Lagrangian inclusions, we establish sufficient optimality conditions for hyperbolic DFIs. Further, the way of extending the obtained results to the multidimensional case is indicated. To demonstrate the above approach, some linear problems and polyhedral optimization with hyperbolic DFIs are investigated.
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Keywords: Hyperbolic inclusions, Euler-Lagrange, Laplace operator, Hamiltonian, equivalence, necessary and sufficient
@article{COCV_2022__28_1_A65_0,
author = {Mahmudov, Elimhan N.},
title = {Optimal control of hyperbolic type discrete and differential inclusions described by the {Laplace} operator},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022061},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022061/}
}
TY - JOUR AU - Mahmudov, Elimhan N. TI - Optimal control of hyperbolic type discrete and differential inclusions described by the Laplace operator JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022061/ DO - 10.1051/cocv/2022061 LA - en ID - COCV_2022__28_1_A65_0 ER -
%0 Journal Article %A Mahmudov, Elimhan N. %T Optimal control of hyperbolic type discrete and differential inclusions described by the Laplace operator %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022061/ %R 10.1051/cocv/2022061 %G en %F COCV_2022__28_1_A65_0
Mahmudov, Elimhan N. Optimal control of hyperbolic type discrete and differential inclusions described by the Laplace operator. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 65. doi: 10.1051/cocv/2022061
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