Optimization of quasilinear complicated systems: case of three determined priorities

This paper is prolongation of researches of mathematical model of the economic system offered in works [1] – [2]. In space $R^n$ three nonnegative nonzero continuous functions $F_i$ ($i= 1, 2, 3$) are set. There is an economic system (for example, the state enterprise). Function $F_3$ describes interior requirements of the system. The economic system is dependent on external “optimizers” (for example, the various ministries). The problem with two exterior “optimizers” is considered in this work. “Optimizer’s” system requirements are described by functions $F_1$ and $F_2$. Interior purposes of the system and “optimizers” does not match in most cases, therefore $F_i$ ($i= 1, 2, 3$) is considered as multidirectional target functions. There is a certain arbiter (governor) who can influence both the system development, and “optimizers”. The arbiter is interested in productive interaction of all structures. According to [1–2] we consider target arbiter function type: $F=F_1^{\alpha_1} F_2^{\alpha_2} F_3^{\alpha_3}$, where $\alpha_1+\alpha_2+\alpha_3$ and $\alpha_i>0$. The determined indicators $\alpha_1$, $\alpha_2$, $\alpha_3$ are called as priorities. Required stationary points conditions of target function and function $F$ local maximum are determined within the limits of the offered quasilinear model.