On Use of the Method of Dynamic Programming of Bellman in Economic Tasks

Method of dynamic programming (MDP) of Bellman is exceptionally efficient for solving a wide class of tasks of economic and mathematical modelling. In a number of cases MDP has no alternative. Meanwhile, statements of specialists with respect to correctness of justification of MDP and also with respect to achievements of R. Bellman are contradictory. In any case, that was the situation during the period of activity of R. Bellman and his opponents. Analysis shows that, to a big extent, these contradictions were caused by competition between Soviet and American scientists at the stage of space exploration. MDP ids based on the Bellman's principle of optimality, which could be characterised as purely ingenious. This is an extremely transparent algorithm of the search for global extremum and is ideally fit for capabilities of computing equipment. Heritage of R. Bellman is great: from the optimal management, differential equations and game theory to economy and medicine. At the same time, methodological approaches of R. Bellman are far from orthodox views on mathematics, which partially explains critics in his address. Heritage of R. Bellman (619 articles and 39 books translated into many languages) deserves a thorough study including perspective of his economic and mathematical magnitude.