First Order Convergence Analysis for Sparse Grid Method in Stochastic Two-Stage Linear Optimization Problem

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DOI: 10.4236/ajcm.2011.14036   PDF   HTML     6,955 Downloads   10,337 Views  

Abstract

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.

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S. Chen, "First Order Convergence Analysis for Sparse Grid Method in Stochastic Two-Stage Linear Optimization Problem," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 294-302. doi: 10.4236/ajcm.2011.14036.

Conflicts of Interest

The authors declare no conflicts of interest.

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