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

Hernan Leoevey (hernaneugenio.leoevey***at***axpo.com)
Werner Roemisch (romisch***at***math.hu-berlin.de)

Abstract: 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 integrands 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.

Keywords: stochastic programming, two-stage, mixed-integer, Quasi-Monte Carlo, effective dimension

Category 1: Stochastic Programming


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Entry Submitted: 12/31/2019
Entry Accepted: 12/31/2019
Entry Last Modified: 05/04/2020

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