Automatic Convexity Deduction for Efficient Function’s Range Bounding
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 traditi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/134 |
| _version_ | 1827602518047195136 |
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| author | Mikhail Posypkin Oleg Khamisov |
| author_facet | Mikhail Posypkin Oleg Khamisov |
| author_sort | Mikhail Posypkin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T05:18:31Z |
| format | Article |
| id | doaj.art-c7d44a19434f4271845f091afe980d1d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:18:31Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c7d44a19434f4271845f091afe980d1d2023-12-03T12:42:54ZengMDPI AGMathematics2227-73902021-01-019213410.3390/math9020134Automatic Convexity Deduction for Efficient Function’s Range BoundingMikhail Posypkin0Oleg Khamisov1Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova 44-2, 119333 Moscow, RussiaMelentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Lermontov St., 130, 664033 Irkutsk, RussiaReliable 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.https://www.mdpi.com/2227-7390/9/2/134interval analysisfunction approximationglobal optimizationconvexity evaluationoverestimatorsunderestimators |
| spellingShingle | Mikhail Posypkin Oleg Khamisov Automatic Convexity Deduction for Efficient Function’s Range Bounding Mathematics interval analysis function approximation global optimization convexity evaluation overestimators underestimators |
| title | Automatic Convexity Deduction for Efficient Function’s Range Bounding |
| title_full | Automatic Convexity Deduction for Efficient Function’s Range Bounding |
| title_fullStr | Automatic Convexity Deduction for Efficient Function’s Range Bounding |
| title_full_unstemmed | Automatic Convexity Deduction for Efficient Function’s Range Bounding |
| title_short | Automatic Convexity Deduction for Efficient Function’s Range Bounding |
| title_sort | automatic convexity deduction for efficient function s range bounding |
| topic | interval analysis function approximation global optimization convexity evaluation overestimators underestimators |
| url | https://www.mdpi.com/2227-7390/9/2/134 |
| work_keys_str_mv | AT mikhailposypkin automaticconvexitydeductionforefficientfunctionsrangebounding AT olegkhamisov automaticconvexitydeductionforefficientfunctionsrangebounding |