期刊
JOURNAL OF GLOBAL OPTIMIZATION
卷 48, 期 3, 页码 473-495出版社
SPRINGER
DOI: 10.1007/s10898-009-9502-3
关键词
Global optimization; Non-convex optimization; Continuous problems; Approximation algorithms; Geometric branch-and-bound; Facility location problems
Geometric branch-and-bound solution methods, in particular the big square small square technique and its many generalizations, are popular solution approaches for non-convex global optimization problems. Most of these approaches differ in the lower bounds they use which have been compared empirically in a few studies. The aim of this paper is to introduce a general convergence theory which allows theoretical results about the different bounds used. To this end we introduce the concept of a bounding operation and propose a new definition of the rate of convergence for geometric branch-and-bound methods. We discuss the rate of convergence for some well-known bounding operations as well as for a new general bounding operation with an arbitrary rate of convergence. This comparison is done from a theoretical point of view. The results we present are justified by some numerical experiments using the Weber problem on the plane with some negative weights.
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