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On importance sampling in the problem of global optimization. (English) Zbl 1173.65002

Summary: 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 parameter depending function, we can assess the maximum of the objective function from the respective sample.

MSC:

65C05 Monte Carlo methods
62K05 Optimal statistical designs
90C15 Stochastic programming
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