Dual Task for the Ecological and Economic Inter-Industry Balance Model with Non-Linear Dependence and Monotonously Decomposable Operator

Abstract

The paper deals with the dual task for the ecological and economic inter-industry balance model with non-linear dependencies which can be described by the system of non-linear equations with monotonously decomposable operators. The suggested model is the equilibrium prices model in which the costs of harmful wastage utilization and recycling are considered. Besides, there are non-linear interrelations between the branches of production, which allows predicting retail prices for the useful products. This is necessary for economistsanalysts who are engaged in forecasting prices of the manufactured products. The suggested algorithms are based on the application of the theory of duality and operational calculus. The authors study the conditions under which this model is solvable and has a nonnegative solution, if at the same time the given values can be negative. The methods of creation of bilateral estimated solutions are adapted for the model; the method of improvement of bilateral estimation is offered. Unlike the methods of searching the precise solution, the application of the method of bilateral estimation facilitates successful solution of tasks with big dimension of the processed models, without resorting to direct integration. The results of this paper can be used in solution of specific tasks of mathematics, economy, biology and other tasks with non-linear interrelations.