Automatic Convexity Deduction for Efficient Function’s Range Bounding

Mikhail Posypkin and Oleg Khamisov
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Mikhail Posypkin: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova 44-2, 119333 Moscow, Russia
Oleg Khamisov: Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Lermontov St., 130, 664033 Irkutsk, Russia

Mathematics, 2021, vol. 9, issue 2, 1-16

Abstract: Reliable bounding of a function’s range is essential for deterministic global optimization, approximation, locating roots of nonlinear equations, and several other computational mathematics areas. Despite years of extensive research in this direction, there is still room for improvement. The traditional and compelling approach to this problem is interval analysis. We show that accounting convexity/concavity can significantly tighten the bounds computed by interval analysis. To make our approach applicable to a broad range of functions, we also develop the techniques for handling nondifferentiable composite functions. Traditional ways to ensure the convexity fail in such cases. Experimental evaluation showed the remarkable potential of the proposed methods.

Keywords: interval analysis; function approximation; global optimization; convexity evaluation; overestimators; underestimators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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