Automatic Convexity Deduction for Efficient Function’s Range Bounding
Reliable bounding of a functionв'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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Библиографическая ссылка
Posypkin M., Khamisov O. Automatic Convexity Deduction for Efficient Function’s Range Bounding // Mathematics. Vol.9. No.2. ID:134. 2021. P.1-15. DOI: 10.3390/math9020134
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