Optimization of structural dynamics of the economy in the framework of the “input-output” methodology

Abstract

The dynamic input-output balance model in the form of a system of differential equations, being digitized by the already published author's methodology, allows solving a wide range of problems of static structural stability of economic systems. Structural dynamics can be optimized by including any variable parameters in the vector and the limit of all model elements. In this paper, inter-sectoral inertias are chosen, and a method is proposed that uses a vector of parameters of an arbitrary (allowed by the model itself) length at the step of the search process. This distinguishes the proposed method from existing ones, making it unique. The uniqueness specified here lies in the removal of the so-called “curse of dimensionality” inherent in the classical optimization problems (numerical search problems) using methods from the coordinate-wise descent to the rich Newtonian-type tools. In this sense, the method is a competitor to machine learning-based optimization of artificial neural networks. At the same time, it does not matter how exactly the task is formalized: it should highlight the target indicators and the vector of variable parameters. It is possible to define and solve many optimization problems by changing the content of the vector of variable parameters according to the corresponding plan of the computational experiment. The paper presents only one example and one optimization stage. The limiting and functional conditions for the operation of the method preserve a linear relationship between the desired increments of the fundamental parts of the eigenvalues of the model state matrix and their sensitivities to control parameters. Such “small” optimization steps are separate and independent problems, the numerical solution of which can be repeated.