单阶段随机规划的一种近似精确罚函数法

An Approximate exact Penalty Function Method for Solving Single Stage Stochastic Programming

提出了一种求解单阶段随机规划的近似精确罚函数法。该法首先对随机变量（连续型）离散化得到一随机变量序列，而将原问题转化为确定性规划问题，再对此规划构造一个精确罚函数。通过求出该罚函数的最优解，可得到随机变量离散后的确定性规划的解从而避免了随着变量离散精度的提高而带来的确定性规划的约束条件个数迅速增加等困难。在一定条件下，我们证明了罚函数的解与确定性规划的解之间的某种等价性。

This paper presents an approximate exact penalty function method for solving single stage stochastic programming. Firstly, obtaining a random vanable sequences by means of discrete random vanable method, to transform original problem into determinite nonlinear programe problem. Secondly constructing an exact penalty function according to this determinite programming, solution of the determinite programming with discreting random vanable can be obtained, through optimal solution of this penalty function. thus difficulties of rapidly growing of the number of constramts of the determinite programming due to increasing of the discreting random variable precisions may be avoided. Under some conditions, some equivalence properties between the solution of the penalty function and the solution of the determinite programming are proved, and the discreting solution sequences epi convergence to the solution of the original problem is proved.