Branch and probability bound methods for global optimization

Article type: Research Article

Authors: Zhigljavsky, Anatoly

Affiliations: Dep. of Mathematics, Leningrad University, 198904 Petrodvorets-Leningrad, Bibliotechnaya pl. 2, USSR

Abstract: The maximization problem for an objective function f given on a feasible region X is considered, where X is a compact subset of Rn and f belongs to a set of continuous multiextremal functions on X can be evaluated at any point x in X without error, and its maximum M=max x∈Xf(x) together with a maximizer x*(a point x* in X such that M=f(x*)) are to be approximated. We consider a class of the global random search methods, underlying an apparatus of the mathematical statistics and generalizing the so-called branch and bound methods.

Keywords: global optimization, random search, branch and bound, statistical inferences

DOI: 10.3233/INF-1990-1108

Journal: Informatica, vol. 1, no. 1, pp. 125-140, 1990