Search schemes for random optimization algorithms that preserve the asymptotic distribution

Abstract

Markovian algorithms for estimating the global maximum or minimum of real valued functions defined on some domain Ω ⊂ ℝ d are presented. Conditions on the search schemes that preserve the asymptotic distribution are derived. Global and local search schemes satisfying these conditions are analysed and shown to yield sharper confidence intervals when compared to the i.i.d. case.