Geodesic
Numerical Solution of an Optimal Control Problem Governed by a Linear Elliptic Equation with Non-Local State Constraints
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 129-144

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An elliptic optimal control problem with distributed control, pointwise control constraints and non-local state constraints has been considered. A mesh approximation of the problem has been constructed. The existence and uniqueness of the approximate solution have been established, and the convergence of the approximate solution to the exact one has been proved. The convergence of the two classes of iterative methods of solving the constructed mesh optimal control problem has been studied. The results of the numerical experiments have been compared. The dependence of the convergence rate upon the mesh size and the regularization parameter in the objective functional has been analyzed.
Keywords: linear elliptic equation, optimal control, finite difference approximation, iterative method. 
@article{UZKU_2012_154_3_a12,
     author = {D. G. Zalyalov and A. V. Lapin},
     title = {Numerical {Solution} of an {Optimal} {Control} {Problem} {Governed} by a {Linear} {Elliptic} {Equation} with {Non-Local} {State} {Constraints}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {129--144},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a12/}
}
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D. G. Zalyalov; A. V. Lapin. Numerical Solution of an Optimal Control Problem Governed by a Linear Elliptic Equation with Non-Local State Constraints. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 129-144. http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a12/