Geodesic
Difference methods in problems of the optimal control of the stationary self-action of light beams
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1157-1169

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A discussion is presented of optimization problems arising in the simulation of the propagation of optical radiation in a material medium with different regimes of absorption and field selfaction. Estimates are established for the rate of convergence of difference and projection-difference schemes for the appropriate non-linear differential equations, no prior assumptions being made as to the smoothness of the generalized solutions or compatability conditions for the grid step-sizes. Estimates are also obtained for the rate of convergence of the finite-dimensional approximations to the optimal control problems based on these schemes. 
@article{ZVMMF_1990_30_8_a3,
     author = {M. M. Potapov and A. V. Razgulin},
     title = {Difference methods in problems of the optimal control of the stationary self-action of light beams},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1157--1169},
     publisher = {mathdoc},
     volume = {30},
     number = {8},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a3/}
}
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M. M. Potapov; A. V. Razgulin. Difference methods in problems of the optimal control of the stationary self-action of light beams. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1157-1169. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a3/