Grygorkiv V. Optimization dynamical models of ecological-economic balance

The conception of mathematical modeling of balanced dynamical processes, which are characterized the aggregated development of complex dynamic systems (economic, ecological-economic, technological, biotechnological etc.) is developed. The production functions of maximum output are investigated with the help of optimization (structural) approach and the method of a construction of such production functions is constructed for case of linear problems of optimal planning. The models of optimal economical growth of one- and multi-sector economics with piece-linear production functions are investigated. The model of multi-sector economics with known structure of mutual capital investments is proposed. The sufficient conditions of optimality for general non-smooth problem of optimal control are established. These conditions generalize analogous results for smooth problem of optimal control. The complex of mathematical models of economic growth is proposed. These models are expanded and developed the neoclassi cal models of growth. There are the aggregated models of dynamical ecological-economic balance, economic optimization with the conditions of dynamical ecological-economic balance, economics optimization with ecological-economic criterion of development, optimal distribution of investments in ecological-economic system and optimization model of multi-sector ecological-economic system. The theory and technique of optimization of ecological-economic systems, which are based on use of models of dynamic interbranch ecological-economic balance, has received further development.