2009-10-16Buch DOI: 10.18452/8404
On probabilistic constraints induced by rectangular sets and multivariate normal distributions
 dc.contributor.author Ackooij, W. Van dc.contributor.author Henrion, R. dc.contributor.author Möller, A. dc.contributor.author Zorgati, R. dc.contributor.editor Higle, Julie L. dc.contributor.editor Römisch, Werner dc.contributor.editor Sen, Surrajeet dc.date.accessioned 2017-06-16T20:21:00Z dc.date.available 2017-06-16T20:21:00Z dc.date.created 2009-10-22 dc.date.issued 2009-10-16 dc.date.submitted 2009-09-01 dc.identifier.uri http://edoc.hu-berlin.de/18452/9056 dc.description.abstract In 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.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject stochastic programming eng dc.subject probabilistic constraints eng dc.subject derivative of probabilities of rectangles eng dc.subject water reservoir management eng dc.subject.ddc 510 Mathematik dc.title On probabilistic constraints induced by rectangular sets and multivariate normal distributions dc.type book dc.identifier.urn urn:nbn:de:kobv:11-100101196 dc.identifier.doi http://dx.doi.org/10.18452/8404 local.edoc.container-title Stochastic Programming E-Print Series local.edoc.pages 13 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 2009 local.edoc.container-issue 6 local.edoc.container-erstkatid 2936317-2