Journal of Global Optimization

, Volume 57, Issue 3, pp 771–782

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

Authors

Open AccessArticle

DOI: 10.1007/s10898-012-9961-9

Cite this article as:
Scholz, D. J Glob Optim (2013) 57: 771. 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

Copyright information

© The Author(s) 2012