Geodesic
On the explicit scheme with variable time steps for solving the parabolic optimal control problem
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 3, pp. 376-387

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The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.
Keywords: optimal control, constraint on control, variable step, iterative method. 
@article{UZKU_2016_158_3_a4,
     author = {A. D. Romanenko},
     title = {On the explicit scheme with variable time steps for solving the parabolic optimal control problem},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {376--387},
     publisher = {mathdoc},
     volume = {158},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_3_a4/}
}
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A. D. Romanenko. On the explicit scheme with variable time steps for solving the parabolic optimal control problem. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 3, pp. 376-387. http://geodesic.mathdoc.fr/item/UZKU_2016_158_3_a4/