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2005-08-30Buch DOI: 10.18452/8346
Ambiguous chance constrained problems and robust optimization
dc.contributor.authorErdogan, E.
dc.contributor.authorIyengar, G.
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T20:05:43Z
dc.date.available2017-06-16T20:05:43Z
dc.date.created2006-03-08
dc.date.issued2005-08-30
dc.date.submitted2005-08-03
dc.identifier.urihttp://edoc.hu-berlin.de/18452/8998
dc.description.abstractIn this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of the distributions is of the form $Q = {Q : \rho_p(Q;Q_0) \le \beta}$, where $\rho_p$ denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure $Q_0$. The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subject.ddc510 Mathematik
dc.titleAmbiguous chance constrained problems and robust optimization
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10059939
dc.identifier.doihttp://dx.doi.org/10.18452/8346
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages26
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2005
local.edoc.container-issue17
local.edoc.container-erstkatid2936317-2

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