FEATURES OF THE APPLICATION OF MATHEMATICAL OPTIMIZATION METHODS FOR THE STUDY OF NANOSTRUCTURES BASED ON X-RAY DIFFRACTION DATA

The features of mathematical optimization methods are considered and algorithms for their use are proposed to increase the efficiency of finding extreme values in solving optimization problems. The proposed algorithms are universal in nature, which allows them to be applied in various fields of computational mathematics. As an illustration, the solution of the inverse problem of reflectometry in the framework of a box model of an electron density profile for a liquid crystal film of a block dendrimer is given. The structure of the thin-film layer on the aqueous subphase was also determined from the grazing-incidence diffraction data. The proposed algorithms of optimization methods are implemented within the analytical software package BARD (Basic Analisys of xRay Diffraction).