Journal of Global Optimization

, Volume 57, Issue 3, pp 771–782

Geometric branch-and-bound methods for constrained global optimization problems

Authors

DOI: 10.1007/s10898-012-9961-9

Abstract

Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method using the concept of the rate of convergence in geometric branch-and-bound methods as introduced in some recent publications. Furthermore, some efficient further discarding tests using necessary conditions for optimality are derived and illustrated numerically on an obnoxious facility location problem.

Keywords

Global optimization Geometric branch-and-bound Approximation algorithms Continuous location

Acknowledgments

The author would like to thank Anita Schöbel for fruitful suggestions for improving the paper. Furthermore, the author gratefully acknowledges the anonymous referees for their helpful comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Copyright information

© The Author(s) 2012