Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs
Mathematisch-Naturwissenschaftliche Fakultät
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.
Files in this item