Geodesic
Solution of an elliptic optimal control problem with pointwise and nonlocal state constraints
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 23-34

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We investigate an optimal control problem governed by linear elliptic equation, with pointwise control constraints and pointwise and integral state constraints. We construct finite difference approximation of the problem and prove the existence of its solution and convergence to the exact solution. We also construct and investigate constrained saddle point problem and iterative solution method for this problem and analyze the results of the numerical experiments.
Keywords: elliptic optimal control, state constraint, finite difference approximation, constrained saddle point problem, iterative methods. 
@article{IVM_2017_4_a3,
     author = {A. V. Lapin and D. G. Zalyalov},
     title = {Solution of an elliptic optimal control problem with pointwise and nonlocal state constraints},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {23--34},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_4_a3/}
}
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A. V. Lapin; D. G. Zalyalov. Solution of an elliptic optimal control problem with pointwise and nonlocal state constraints. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 23-34. http://geodesic.mathdoc.fr/item/IVM_2017_4_a3/