Concerning problems of optimization in nonlinear optics

Optimization algorithms for problems of nonlinear optics are presented based on the application of similarity theory and gradient methods of optimal control. Examples of the application of similarity theory to the calculation of nonlinear quasi-optic systems are discussed, including wave diffraction in a medium with a nonlinear refractive index; and coherent wave interaction, and the generation of difference and sum frequencies. It is concluded that the application of similarity theory and optimal control methods makes it possible to considerably simplify and speed up the task of determining relationships between field characteristics and the parameters of the medium and the incident radiation.