Synthesis of effective optimization algorithms and development of the direct Lyapunov method

The issues related to the theoretical justification and practical application of new methods for the synthesis of highly efficient numerical optimization algorithms of the first and second orders are considered. A significant improvement in the convergence rate and expansion of the convergence range of algorithms is provided by adapting the general results of the stabilization theory of discrete non-autonomous controlled systems using the advantages of the theory of limit equations and the Lyapunov function method.