期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2011
卷号：1
期号：4
页码：294-302
DOI：10.4236/ajcm.2011.14036
出版社：Scientific Research Publishing
摘要：Stochastic two-stage linear optimization is an important and widely used optimization model. Efficiency of numerical integration of the second stage value function is critical. However, the second stage value function is piecewise linear convex, which imposes challenges for applying the modern efficient spare grid method. In this paper, we prove the first order convergence rate of the sparse grid method for this important stochastic optimization model, utilizing convexity analysis and measure theory. The result is two-folded: it establishes a theoretical foundation for applying the sparse grid method in stochastic programming, and extends the convergence theory of sparse grid integration method to piecewise linear and convex functions.
关键词：Convergence Analysis; Stochastic Optimization; Scenario Generation; Convex Analysis; Measure Theory
