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2009-10-16Buch DOI: 10.18452/8404
On probabilistic constraints induced by rectangular sets and multivariate normal distributions
dc.contributor.authorAckooij, W. Van
dc.contributor.authorHenrion, R.
dc.contributor.authorMöller, A.
dc.contributor.authorZorgati, R.
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T20:21:00Z
dc.date.available2017-06-16T20:21:00Z
dc.date.created2009-10-22
dc.date.issued2009-10-16
dc.date.submitted2009-09-01
dc.identifier.urihttp://edoc.hu-berlin.de/18452/9056
dc.description.abstractIn this paper, we consider optimization problems under probabilistic constraints which aredefined by two-sided inequalities for the underlying normally distributed random vector. Asa main step for an algorithmic solution of such problems, we derive a derivative formula for(normal) probabilities of rectangles as functions of their lower or upper bounds. This formulaallows to reduce the calculus of such derivatives to the calculus of (normal) probabilitiesof rectangles themselves thus generalizing a similar well-known statement for multivariatenormal distribution functions. As an application, we consider a problem from water reservoirmanagement. One of the outcomes of the problem solution is that the (still frequentlyencountered) use of simple individual probabilistic can completely fail. In contrast, the (more difficult) use of joint probabilistic constraints which heavily depends on the derivative formula mentioned before yields very reasonable and robust solutions over the whole time horizon considered.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.subjectstochastic programmingeng
dc.subjectprobabilistic constraintseng
dc.subjectderivative of probabilities of rectangleseng
dc.subjectwater reservoir managementeng
dc.subject.ddc510 Mathematik
dc.titleOn probabilistic constraints induced by rectangular sets and multivariate normal distributions
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-100101196
dc.identifier.doihttp://dx.doi.org/10.18452/8404
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages13
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2009
local.edoc.container-issue6
local.edoc.container-erstkatid2936317-2

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