Optimization methods in coordinated planning. I. An active system with differentiable functions in the element model

A general problem of coordinated planning in a two-level active system is formulated and its model described. This problem is shown to be akin to numerous problems of optimizing hierarchical systems such as of nonlinear input – output balance, vector optimization, coordination of hierarchical systems, hierarchical resource allocation, and two-level programming, and with hierarchical games in the information theory of hierarchical systems. Two ways to solve this problem by using a first order optimality condition are proposed. Examples are given.