On importance sampling in the problem of global optimization : Monte Carlo Methods and Applications

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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board Member: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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On importance sampling in the problem of global optimization

Trifon I. Missov1 / Sergey M. Ermakov2

1Department of Stochastic Simulation, Saint Petersburg State University, and Max Planck Institute for Demographic Research, Germany. Email:

2Head of the Department of Stochastic Simulation, Saint Petersburg State University, Russia. Email:

Citation Information: Monte Carlo Methods and Applications. Volume 15, Issue 2, Pages 135–144, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/MCMA.2009.007, August 2009

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Importance sampling is a standard variance reduction tool in Monte Carlo integral evaluation. It postulates estimating the integrand just in the areas where it takes big values. It turns out this idea can be also applied to multivariate optimization problems if the objective function is non-negative. We can normalize it to a density function, and if we are able to simulate the resulting p.d.f., we can assess the maximum of the objective function from the respective sample.

Keywords.: Global optimization; importance sampling; Δ2-distribution; D-optimal designs

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