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2012-02-20Buch DOI: 10.18452/8421
Gradient estimates for Gaussian distribution functions: Application to probabilistically constrained optimization problems
dc.contributor.authorHenrion, René
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T20:26:11Z
dc.date.available2017-06-16T20:26:11Z
dc.date.created2012-02-22
dc.date.issued2012-02-20
dc.date.submitted2012-01-15
dc.identifier.urihttp://edoc.hu-berlin.de/18452/9073
dc.description.abstractWe provide lower estimates for the norm of gradients of Gaussian distribution functions and apply the results obtained to a special class ofprobabilistically constrained optimization problems. In particular, it is shown how the precision of computing gradients in such problems can be controlled by the precision of function values for Gaussian distribution functions. Moreover, a sensitivity result for optimal values with respect to perturbations of theunderlying random vector is derived. It is shown that the so-called maximal increasing slope of the optimal value with respect to the Kolmogorov distance between original and perturbed distribution can be estimated explicitly fromthe input data of the problem.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.subjectprobabilistic constraintseng
dc.subjectchance constraintseng
dc.subjectstochastic optimizationeng
dc.subjectGaussian distribution functioneng
dc.subjectsensitivity of optimal valueseng
dc.subject.ddc510 Mathematik
dc.titleGradient estimates for Gaussian distribution functions: Application to probabilistically constrained optimization problems
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-100199486
dc.identifier.doihttp://dx.doi.org/10.18452/8421
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages14
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-publisher-nameAIMS
local.edoc.container-publisher-placeSpringfield
local.edoc.container-volume2012
local.edoc.container-issue1
local.edoc.container-erstkatid2936317-2

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