Abstract
Many theorems in mathematics require a real function to be continuous over the domain under consideration. In particular the Brouwer fixed point theorem and the mean value theorem underlie many interval methods like Newton operators for solving numerical constraint satisfaction problems or global optimization problems. Since the continuity property collapses when the function is not defined at some point it is then important to check whether the function is defined everywhere in a given domain. We introduce here an interval branch-and-contract algorithm that rigorously approximate the domain of definition of a factorable function within a box. The proposed approach mainly relies on interval contractors applied to the domain constraints and their negations stemming from the expression of the function.
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Acknowledgment
The author would like to thank Christophe Jermann for interesting discussions about these topics and his careful reading of a preliminary version of this paper.
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Granvilliers, L. (2020). Filtering Domains of Factorable Functions Using Interval Contractors. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_10
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DOI: https://doi.org/10.1007/978-3-030-21803-4_10
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