On importance sampling in the problem of global optimization

Missov, T. I., Ermakov, S. M.

Monte Carlo Methods and Applications, 15:2, 135-144 (2009)



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.