The monograph develops a new coordination strategy in the theory of hierarchical systems, called non-iterative coordination. Its application solves optimization problems in mathematical programming using a hierarchical approach. To solve such problems, the initial high-dimensional optimization problem is decomposed into a set of lower-dimensional subproblems solved by the subsystems and the coordinator of a two-level hierarchical system. When solving the coordination problem in hierarchical systems theory, two main coordination procedures are applied: coordination with modification of the objectives of the subsystems (target coordination) and coordination with modification of the definition domains or constraints of the subsystem problems (prediction coordination). The research in the monograph mainly concerns prediction coordination with the application of non-iterative coordination. Models of hierarchical systems are presented, and hierarchical solutions to the corresponding optimization tasks are presented. This allows, in certain cases, the solution to the optimization task to be obtained in an explicit analytical form. The hierarchical models developed, the algorithms for solving and the optimization solutions obtained, as well as the practical applications are a result of the further development of the method of non-iterative target coordination, already published as a scientific result in co-authorship with Senior Researcher I, Dr. Todor Stoilov.