## 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

Zbl 0208.22001
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