3. SOME QUASILINEAR MODELS OF COMPLEX SYSTEMS WITH RANDOM PRIORITIES. THE CASE OF TWO
Volosatova, T. A., and A. G. Danekyants. "Some Quasilinear Models of Complex Systems with Random Priorities.
The Case of Two Dependent Priorities." Global and Stochastic Analysis, vol. 12, no. 5, 2025, pp. 18–22.
Abstract
Recently, There is an economic system (for example, a budget organization). The internal requirements of the system
are expressed by a function. The economic system is not independent and is affected by external ”optimizers” (for
are expressed by a function. The economic system is not independent and is affected by external ”optimizers” (for
example, various ministries). We will write the target function of the arbitrator as F = E(Fα11 Fα22). Function F(2)
expresses the internal requirements of the system, and function F(1) the requirements of some external ”optimizers”
expresses the internal requirements of the system, and function F(1) the requirements of some external ”optimizers”
to this system. The internal goals of the system and the goals of the ”optimizers” do not coincide in most cases.
There is a certain arbitrator (regulator) that can influence both the development of the system itself and the
”optimizers”. The main goal of the arbitrator is to set priorities that will ensure the successful functioning of all
divisions of the economic system as a whole. Within the framework of the proposed model, the necessary conditions
for the existence of stationary points of the objective function are obtained and its theorem of the existence and
uniqueness of the global maximum of the objective function F is proven.
Keywords
Key words and phrases. quasi-linear models, optimization problem, priorities, extremum of the function.