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

• 成果类型: Article
• 署名作者: Leovey, H.; Roemisch, W.
• 署名单位: Humboldt University of Berlin
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01538-6
• 发表日期: 2021
• 页码: 361-392
• 关键词: high-dimensional integration; shifted lattice rules; CONVERGENCE; variance; CONSTRUCTION; algorithms; STABILITY

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.