2005-08-30Buch DOI: 10.18452/8346
Ambiguous chance constrained problems and robust optimization
 dc.contributor.author Erdogan, E. dc.contributor.author Iyengar, G. dc.contributor.editor Higle, Julie L. dc.contributor.editor Römisch, Werner dc.contributor.editor Sen, Surrajeet dc.date.accessioned 2017-06-16T20:05:43Z dc.date.available 2017-06-16T20:05:43Z dc.date.created 2006-03-08 dc.date.issued 2005-08-30 dc.date.submitted 2005-08-03 dc.identifier.uri http://edoc.hu-berlin.de/18452/8998 dc.description.abstract In 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.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.subject.ddc 510 Mathematik dc.title Ambiguous chance constrained problems and robust optimization dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10059939 dc.identifier.doi http://dx.doi.org/10.18452/8346 local.edoc.container-title Stochastic Programming E-Print Series local.edoc.pages 26 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 2005 local.edoc.container-issue 17 local.edoc.container-erstkatid 2936317-2