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What can interval analysis do for global optimization?

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Abstract

An overview of interval arithmetical tools and basic techniques is presented that can be used to construct deterministic global optimization algorithms. These tools are applicable to unconstrained and constrained optimization as well as to nonsmooth optimization and to problems over unbounded domains. Since almost all interval based global optimization algorithms use branch-and-bound methods with iterated bisection of the problem domain we also embed our overview in such a setting.

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  1. Mathematisches Institut, Heinrich Heine Universität, 4000, Düsseldorf, Germany

    H. Ratschek & R. L. Voller

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  1. H. Ratschek
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  2. R. L. Voller
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Ratschek, H., Voller, R.L. What can interval analysis do for global optimization?. J Glob Optim 1, 111–130 (1991). https://doi.org/10.1007/BF00119986

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