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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机译：Análisis no-lineal de la convergencia regional en América Latina, 1950-2010: un modelo panel TAR↓Analyse non linéaire de la convergence régionale latino-américaine, 1950-2010: un modèle panel TAR↓Análise n?o-linear da convergência regional na América Latina, 1950-2010: um modelo panel TAR↓基于面板阈值自回归模型（TAR）对1950-2010年拉丁美洲区域趋同的非线性分析
机译：metodi microbiologici Tradizionali e metodi moleculeolari per l'analisi degli integratori alimentari a base di o con probiotici per ujso umano（microbiological and molecular methods for analysis of probiotic Based Food supplements for Human Consumption）。
