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2014-12-30Buch DOI: 10.18452/8444
Quasi-Monte Carlo methods for linear two-stage stochastic programming problems
dc.contributor.authorLeövey, Hernan
dc.contributor.authorRömisch, Werner
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T20:32:12Z
dc.date.available2017-06-16T20:32:12Z
dc.date.created2015-02-11
dc.date.issued2014-12-30
dc.date.submitted2014-11-01
dc.identifier.urihttp://edoc.hu-berlin.de/18452/9096
dc.description.abstractQuasi-Monte Carlo algorithms are studied for generating scenarios to solve two-stage linear stochastic programming problems. Their integrands are piecewise linear-quadratic, but do not belong to the function spaces consideredfor QMC error analysis. We show that under some weak geometric condition on the two-stage model all terms of their ANOVA decomposition, except the one of highest order, are continuously differentiable and second order mixed derivativesexist almost everywhere and belong to $L_2$. This implies that randomly shifted latticerules may achieve the optimal rate of convergence $O(n^{-1+\delta})$ with $\delta \in (0,\frac{1}{2}]$ and a constant not depending on the dimension if the effective superposition dimension is less than or equal to two. The geometric condition is shown to be satisfied for almost all covariance matrices if the underlying probability distribution isnormal. We discuss effective dimensions and techniques for dimension reduction.Numerical experiments for a production planning model with normal inputs showthat indeed convergence rates close to the optimal rate are achieved when usingrandomly shifted lattice rules or scrambled Sobol' point sets accompanied withprincipal component analysis for dimension reduction.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleQuasi-Monte Carlo methods for linear two-stage stochastic programming problems
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-100226458
dc.identifier.doihttp://dx.doi.org/10.18452/8444
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages28
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2014
local.edoc.container-issue6
local.edoc.container-erstkatid2936317-2

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