Dynamic Programming Problem In Mathematics Modelling

The method of Dynamic Programming was originally proposed in the 1950s, and Richard Bellman introduced it the most optimized principle which had laid a solid foundation for the method. The Dynamic Programming has played the most important role in the area such as operations research, cybernetics, management science development in the past 50 years, and it became one of the most commonly used optimization methods in solving mathematics modelling questions. But as an important optimized method, it has too many questions which urgently await to be solved that expose its imperfection. Therefore, in the process of utilizing this method, people have devoted a lot to perfect the condition of applying Dynamic Programming as well as the solution method of Dynamic Programming questions. This article has conducted the deep research and the summary to the Dynamic Programming in the past 50 years'development, specially paid attention to the study of its various newly algorithms. Such as the analysis law of deterministic univariate Dynamic Programming, computation method; the deterministic multi-dimensional Dynamic Programming's Lagrange multiplier, iterates, the strategy and the function space approximation, the multinomial approaches, hyper-surface; the base algorithm of stochastic Dynamic Programming and so on. At the end of the article, I solved a mathematics modelling problem through the use Dynamic Programming method, in order to manifest the superiority of Dynamic Programming in the practical application.