This monograph is a concise explanation of recent advances, obtained by scientific workers of Eastern European countries, in the field of optimization and its application in the area of mathematical economy and control of economic systems. Light is thrown on a variety of problems concerned with the construction and analysis of optimization models: equilibrium models of mathematical economy, modern numerical optimization methods and software, methods of convex programming optimal with respect to complexity, polynomial algorithms of linear programming, decomposition of optimization systems, modern apparatus of nonsmooth optimization, models and methods of discrete programming. Special attention is paid to extensions of the optimization approach - to the analysis and correction of inconsistent mathematical programming problems, multiobjective problems, optimization in order scales, and to extremal problems in infinite-dimensional spaces.