Difference methods in problems of the optimal control of the steady selfaction of light beams

Abstract

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.