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Author (up) Barrera, J.; Homem-De-Mello, T.; Moreno, E.; Pagnoncelli, B.K.; Canessa, G. pdf  doi
  Title Chance-constrained problems and rare events: an importance sampling approach Type
  Year 2016 Publication Mathematical Programming Abbreviated Journal Math. Program.  
  Volume 157 Issue 1 Pages 153-189  
  Keywords Chance-constrained programming; Sample average approximation; Importance sampling; Rare-event simulation  
  Abstract We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.  
  Address [Barrera, Javiera; Moreno, Eduardo] Univ Adolfo Ibanez, Fac Sci & Engn, Santiago, Chile, Email:  
  Corporate Author Thesis  
  Publisher Springer Heidelberg Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0025-5610 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000375568400007 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 613  
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