Chaining via annealing (Q1175412)

The aim of the paper is the numerical evaluation of \(\int_X f(x)\mu\,(dx)\) where \(X\) is a metric space, \(\mu\) is a measure on the Borel sets and \(f\colon X\to \mathbb{R}\) is Borel measurable. A very general method of implementing chaining for such arbitrary integrals is presented. Further it is shown that the chaining can be applied to solve global optimization problems. Also, several generalizations of a theorem of \textit{M. Pincus} [Oper. Res. 16, 690--694 (1968; Zbl 0208.22001)] are given.