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Chaining via annealing. (English) Zbl 0739.65119
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 M. Pincus [Oper. Res. 16, 690–694 (1968; Zbl 0208.22001)] are given.
MSC:
65C99 Probabilistic methods, stochastic differential equations
65D32 Numerical quadrature and cubature formulas
65J05 General theory of numerical analysis in abstract spaces
62D05 Sampling theory, sample surveys
65C05 Monte Carlo methods
90C27 Combinatorial optimization
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