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Chance-constrained problems and rare events: an importance sampling approach

Javiera Barrera(javiera.barrera***at***uai.cl)
Tito Homem-de-Mello(tito.hmello***at***uai.cl)
Eduardo Moreno(eduardo.moreno***at***uai.cl)
Bernardo K. Pagnoncelli(bernardo.pagnoncelli***at***uai.cl)
Gianpiero Canessa(gianpiero.canessa***at***uai.cl)

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. Using a Sample Average Approximation (SAA) approach combined with importance sampling (IS) techniques, we show how variance can be reduced uniformly over a suitable approximation of the feasibility set, and as a result the problem can be solved with much fewer samples. We provide sufficient conditions to obtain such uniform variance reduction and prove asymptotic convergence of the combined SAA-IS approach. We apply our methodology to a telecommunications problem, find IS distributions that satisfy the conditions laid out for uniform variance reduction in that context and present numerical results to illustrate the ideas.

Keywords: Chance-constrained programming, Sample Average Approximation, Importance sampling, Rare-event simulation

Category 1: Stochastic Programming

Citation: Universidad Adolfo IbaƱez, Feb 2014.

Download: [PDF]

Entry Submitted: 02/26/2014
Entry Accepted: 02/26/2014
Entry Last Modified: 02/26/2014

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