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SPEPS Preprint

 Author(s): E. Erdogan, Columbia UniversityG. Iyengar, Columbia University Title: Ambiguous chance constrained problems and robust optimization Date of Acceptance: 30.08.2005 Submission Date: 03.08.2005 Series Title: Stochastic Programming E-Print Series (SPEPS) Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen Complete Preprint: pdf (urn:nbn:de:kobv:11-10059939) Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex print on demand: If you click on this icon you can order a print copy of this publication.

Abstract (eng):
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.
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