Study Of Some Algorithms For Multi-Stage Stochastic Program And Its Applications

This paper introduces the development of stochastic programming systematically while summarizing and analyzing the fruits on this field during the past. Based on the study of some researchers, we study several new algorithms and its applications for multi-stage stochastic programming, especially on how to apply benders decomposition and SQP decomposition to multi-stage stochastic programming. The whole paper contains four chapters, and it is arranged as follows:In the first chapter, we summarily introduce the development and the current research situation as well as classification stochastic programming.In the second chapter, two efficient algotithms to solve multi-stage stochastic programming are developed:Benders decomposition and primal-dual decomposition algorithm based on cutting plane methods. we compare with the above algorithm, and give the generic thought and the next direction of research.In the third chapter, we give a decomposition method based on SQP for multi-stage stochastic programs. when the realization of the random variable are very large, we can decompose the primal problem into a series of small-scale quadratic programs, and the algorithm posses the global convergence.In the last chapter, with stochastic programming theory and based on production and supply plan, we give a stochastic programming model. we solve this model with the algorithm in the second chapter. Numerical results illustrate the efficiency of the algorithm.