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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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Volume 15, Issue 2 (Jan 2009)


On importance sampling in the problem of global optimization

Trifon I. Missov
  • Department of Stochastic Simulation, Saint Petersburg State University, and Max Planck Institute for Demographic Research, Germany. Email:
/ Sergey M. Ermakov
  • Head of the Department of Stochastic Simulation, Saint Petersburg State University, Russia. Email:
Published Online: 2009-08-19 | DOI: https://doi.org/10.1515/MCMA.2009.007


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

About the article

Received: 2008-07-14

Revised: 2008-12-15

Published Online: 2009-08-19

Published in Print: 2009-08-01

Citation Information: Monte Carlo Methods and Applications, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/MCMA.2009.007. Export Citation

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