Geodesic
Penalty method for the state equation for an elliptical optimal control problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 36-48

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We solve an optimal control problem of a system governed by a linear elliptic equation with pointwise control constraints and non-local state constraints by finite difference method. A discrete optimal control problem is approximated by a minimization problem with penaltized state equation. We derive an error estimates. We also prove the rate of convergence of block Gauss–Zeidel iterative solution method for the penaltized problem. We present the results of the numerical experiments.
Keywords: constraint saddle point problem, optimal control, finite difference approximation, iterative methods. 
@article{IVM_2015_7_a3,
     author = {A. V. Lapin and D. G. Zalyalov},
     title = {Penalty method for the state equation for an elliptical optimal control problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--48},
     publisher = {mathdoc},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_7_a3/}
}
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A. V. Lapin; D. G. Zalyalov. Penalty method for the state equation for an elliptical optimal control problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 36-48. http://geodesic.mathdoc.fr/item/IVM_2015_7_a3/