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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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