基于SQP的两阶段随机规划的算法研究

发布时间：2018-08-10 07:45

【摘要】：随机规划是求解不确定环境下最优化问题的基本方法。两阶段随机规划问题是依据随机变量被观测到具体取值的前后,把决策变量和过程分成两阶段来进行决策的数学规划。本文基于序列二次规划(Sequential quadratic programming,简称SQP)理论,研究了两类随机非线性规划的求解算法。本文研究SQP法求解两阶段随机规划,主要用于求解补偿型随机非线性规划和线性部分信息(Linear partial information,简称LPI)随机非线性规划。对于补偿型随机非线性规划,本文在SQP方法的基础上,结合积极集方法求解二次规划子问题,得到搜索方向,同时为了避免选取罚因子的困难,用滤子方法得到步长,给出了两类补偿型随机非线性规划的求解算法,在文中假设下给出了算法的收敛性,并通过数值算例表明了算法的有效性。对于LPI随机非线性规划,本文结合上述补偿型随机非线性规划的技巧,得到了LPI随机非线性规划的新算法,并且给出了算法的收敛性。本文给出的三种求解随机非线性规划的新算法可以组成一个算法系统,对于一般的中小规模随机非线性规划都可以给出求解思路。
[Abstract]:Stochastic programming is a basic method for solving optimization problems in uncertain environments. The two-stage stochastic programming problem is a mathematical programming that divides the decision variables and the process into two stages according to the observed values of the random variables. Based on the theory of sequential quadratic programming (Sequential quadratic programming,), two kinds of stochastic nonlinear programming algorithms are studied in this paper. In this paper, we study the SQP method for solving two-stage stochastic programming, which is mainly used to solve compensatory stochastic nonlinear programming and linear partial information (Linear partial information, (LPI) stochastic nonlinear programming. For compensatory stochastic nonlinear programming, in this paper, based on the SQP method, the quadratic programming subproblem is solved with the positive set method, and the search direction is obtained. In order to avoid the difficulty of selecting penalty factors, the filter method is used to obtain the step size. In this paper, two kinds of compensatory stochastic nonlinear programming algorithms are given. The convergence of the algorithm is given under the assumption in this paper, and the validity of the algorithm is demonstrated by numerical examples. For LPI stochastic nonlinear programming, a new algorithm for LPI stochastic nonlinear programming is obtained and the convergence of the algorithm is given by combining the above techniques of compensatory stochastic nonlinear programming. In this paper, three new algorithms for solving stochastic nonlinear programming can be used to form an algorithm system, which can be used to solve small and medium scale stochastic nonlinear programming.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221

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