The basic terms and relations of optimal control theory, analytical and numerical methods of one dimensional and multidimensional static optimization and classical theory of extreme regulation of dynamic systems are discussed. Attention is also paid to the optimal management of larger technological units using linear programming. The lecture is focused on the principles of dynamic optimization and the use of artificial intelligence. The subject provides comprehensive information on the problems of calculating the extremes of functions and functions in solving the optimization tasks of controlling technological aggregates and processes.