1993 | OriginalPaper | Chapter
The Cluster Problem in Global Optimization: the Univariate Case
Authors : B. Kearfott, K. Du
Published in: Validation Numerics
Publisher: Springer Vienna
Included in: Professional Book Archive
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The Cluster Problem in Global Optimization the Univariate Case. We consider a branch and bound method for enclosing all global minimizers of a nonlinearC2 or C1 objective function. In particular, we consider bounds obtained with interval arithmetic, along with the “midpoint test,” but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undesirable Cluster of intervals around each minimizer. In this article, we analyze this problem in the one dimensional case. Theoretical results are given which show that the problem is highly related to the behavior of the objective function near the global minimizers and to the order of the corresponding interval extension.