On calculating of functional derivative for an optimal control problem

The synthesis problem of a multilayer diffraction grating is formulated as an optimal control problem and consists in minimizing the cost functional depending on the geometric parameters of the grating profile. The gradient method is the most reliable and stable method for solving this problem. The paper deals with a method for calculating the gradient of the cost functional, which is done by solving a cojugate problem with special boundary conditions. Additionally, the paper discusses the numerical implementation of this solution and the calculation of the gradient. The results from a computational experiment are also presented.