随机规划的逼近方法

Approximation Method for Stochastic Programming

本文将随机函数V（x，ω）引入随机规划问题·即Z（V（ω））■，对相应的最优化问题的稳定性作了一些探讨．得出了在一定条件下．只要Vn（ω）个分布收敛于v（ω），最优值Z（Vn（ω）就收敛于Z（v（ω）的结果，这个结论对于构造逼近算法，特别是如何估计逼近误差和改进逼近值提供了理论依据。

The general form of stochastic programming is:Z(V (ω)) =■Where V(ω)is a random variable or a random veotor.In this paper random funxtion V(x,ω) is brought into stochatic programming problem and the stability of the corresponding optimiation problems are aualysed. Then excellent results are derived which the optimal value Z (V. (ω)) convergences to Z (V (ω) if Vn (ω) convergences to V(ω) in distibuction. It provides the theoriticd base for Constucting approximate algorthms, especially for estimating approximcotion error and improving approximate value.