Geodesic
Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1767-1792

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Mathematical formulations of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching conditions are examined. Finite difference approximations of optimization problems are constructed, and the approximation error is estimated with respect to the state and the cost functional. Weak convergence of the approximations with respect to the control is proved. The approximations are regularized using Tikhonov regularization. 
@article{ZVMMF_2014_54_11_a7,
     author = {F. V. Lubyshev and A. R. Manapova and M. E. Fairuzov},
     title = {Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1767--1792},
     publisher = {mathdoc},
     volume = {54},
     number = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a7/}
}
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F. V. Lubyshev; A. R. Manapova; M. E. Fairuzov. Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1767-1792. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a7/