Some Problems On Stochastic Programming

On the foundation of systematically analyzing and summarizing the stochastic programming problems which are one of the most attractive problems in mathematical programming area in recent years. Based on the viewpoint of optimization, it further discusses the essence of stochastic programming and its algorithm concentrated on.In the first place, I briefly review the development and the current research situations of the stochastic programming as well as classification about the stochastic programming. At the same time, I introduce some topic in the following chapters.In the second chapter, a new Wolfe-BFGS-SQP method based on the Quasi-Monte-Carlo stochastic simulation for the two-stage stochastic programming with recourse is presented. At the same time , the Wolfe line search for the BFGS-SQPmethod is involved for solving the LC1 optimization method. In particular, the newmethod can reduce calculating amount. At last, its global convergence and its superlinear convengence have been shown.In the third chapter, a sequential quadratically constrained quadratic programming (SQCQP) method based on the Quasi-Monte-Carlo stochastic simulation for two stage convex stochastic programming with quadratically constrained condition is presented .At the same time, its global convergence and its local quadratic rate of convengence have been shown. In particular, it has been shown that the Maratos effect can be avoided .In the forth chapter, the fuzzy time series model has been changed into the chance constrained programming. At the same time, this programming is solved by an improved genetic algorithm based on the Monte Carlo stochastic simulation.