Importance The article studies an economic region as a unit of administrative and territorial division of the first-level classification (Republic, Krai, Region and District). The research considers the sustainable development of an economic region as the "population - economy - nature" triad. Objectives The article aims to develop the method of mathematical models application of optimal management while researching the issues of the sustainable development of economic region as one of the methods of scientific cognition, which enables to use the unique mathematical apparatus to conduct the preliminary quantitative and qualitative experiments and obtaining of substantiated recommendations on the selection of optimal priorities and corresponding strategy. Methods The goal of the research is achieved by solving the following tasks: systematization and actualization of the basic principles, conditions and constraints of the sustainable development concept as a new formation for the human society development; formalization of the sustainable development issue for economic region in the form of dynamic process model with many management parameters and quality criteria; the research of academic questions (existence of the sustainable development path, establishment of the necessary and/or sufficient features for optimality of the sustainable development strategy; approbation of the theoretical results by the example of mathematical model for sustainable development (the Mir-3 model modification). We analyze the possibility of the research of the sustainable development issues for economic region on the basis of mathematical modeling as unique way of scientific cognition, which is proved to be well-grounded, viable and practically useful. Results The article contains the mathematical models elaboration for optimal management when carrying out the quantitative and qualitative research of the sustainable development issues for the economic region. Conclusions and Relevance We have developed practical recommendations, obtained as the mathematical results interpretation using the language of the sustainable development concept, which refer to such key issues of regional development as goal-setting, choice of preferable development scenario, positional management actions, optimal financial means distribution, etc.
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