Study Of Some Decomposotion Algorithms For Stochastic Programs 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 decomposition algorithms and its applications, especially on how to solve the stochastic programming with dispersed random variable, The whole paper contains five 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 ,we solve the convex programming with the Benders decomposition algorithm, for example the two-stage stochastic programming .This algorithm make use of the convexity and the thought of approach, and we can gain the optimal solution or the approximate optimal solution with any desirable accuracy quickly.In the third chapter, we introduction a primal-dual decomposition algorithm based on the interior point approach. This algorithm translate the primal programs into solving the direction-finding sub-problem at each iteration based on the homogeneous self-dual technique. This algorithm allow one to freely select any interior starting point ( possibly infeasible),and this is very important for stochastic programs. we compare with the above algorithm, and give the generic thought and the next direction of research.In the fourth 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 decomposition 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 above algorithm.