The Study Of Some Algorithms For Stochastic Programs And Its Applications

Interior-point (IP) methods have proved to be very successful in solving nonlinear programming problems (NLP). The basic scheme of an IP method is in the following: for a series of penalty parameters μ(μ > 0 and μ →0), solve a series of nonlinear programming problems, noted by P_μ ; for fixed μ , find an approximate solution or an exact solution x~*(μ,) to P_μ. How to solve the problem P_μ has been the research focus by some researchers. Chapter 2 in this paper introduces the sequential systems of linear equations (SSLE) method to solve P_μ and gives the whole scheme of the IP method and the corresponding convergence.The rest of this paper is organized as follows. Chapter 3 applies the method in Chapter 2 into two-stage stochastic programs with recourse, generating the observations by Monte-Carlo (MC) method or by Quasi Monte-Carlo (QMC) method respectively. Chapter 4 gives a lagrange-Newton method for two-stage stochastic programs with recourse,generating the observations by QMC method. Chapter 5 gives a survey on robust technology in optimization problems with uncertainty. The basic scheme, goal of robustness, and solving approach — dual program are introduced. At the end of this chapter, a simple overview about robust technology in applications is given.