Multilevel iterative schemes of numerical optimization (Q1920369)

The author describes a class of numerical methods for mathematical programming problems and problems of the solution of equations based on the approximation of the initial problem to a collection of simpler problems ordered with respect to their complexities. The class of methods in question is described in the form of a general iterative scheme, the concrete definition of which allows one to obtain new methods, as well as classical numerical methods of Newton type. The proposed methods are aimed at a reduction of the computation expenditures for the solution of complex problems of mathematical programming. Some problems of global optimization of nonconvex functions, problems of statistical optimization of parameters of control algorithms, identification problems, problems of terminal control, and other problems of this kind constitute promising directions of the application of suggested multilevel schemes.