Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs

作     者：Leovey, H. Roemisch, W. 

作者机构：Axpo Struct Energy Management Team Baden Switzerland Humboldt Univ Inst Math Berlin Germany 

出 版 物：《MATHEMATICAL PROGRAMMING》 (数学规划)

年 卷 期：2021年第190卷第1-2期

页      面：361-392页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 

基　　金：Projekt DEAL 

主　　题：Stochastic programming Two-stage Mixed-integer Sampling Quasi-Monte Carlo Haar measure 

摘      要：We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optimal value function is piecewise linear-quadratic with possible kinks and discontinuities at the boundaries of certain convex polyhedral sets. This structure is exploited to provide conditions implying that first and higher order terms of the integrand s ANOVA decomposition (Math. Comp. 79 (2010), 953-966) have mixed weak first order partial derivatives. This leads to a good smooth approximation of the integrand and, hence, to good convergence rates of randomized QMC methods if the effective (superposition) dimension is low.