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A piecewise smooth version of the Griewank function.

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Title: A piecewise smooth version of the Griewank function.
Authors: Bosse, Torsten F.1 (AUTHOR) torsten.bosse@uni-jena.de, Bücker, H. Martin1 (AUTHOR)
Source: Optimization Methods & Software. Apr2026, Vol. 41 Issue 2, p347-357. 11p.
Subjects: Nonsmooth optimization, Mathematical functions, Deep learning, Global optimization, Cost functions
Abstract: The Griewank test function for global unconstrained optimization has multiple local minima clustered around the global minimum at the origin. A new version of this test function is proposed that has a similar structure, but whose behavior at the local minima and maxima is non-smooth. This piecewise smooth version of the Griewank function represents an abs-factorable test case of objective functions for global non-smooth optimization as, for example, observed in the training of neural networks. [ABSTRACT FROM AUTHOR]
Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A piecewise smooth version of the Griewank function.
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  Data: <searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Global+optimization%22">Global optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink>
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  Label: Abstract
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  Data: The Griewank test function for global unconstrained optimization has multiple local minima clustered around the global minimum at the origin. A new version of this test function is proposed that has a similar structure, but whose behavior at the local minima and maxima is non-smooth. This piecewise smooth version of the Griewank function represents an abs-factorable test case of objective functions for global non-smooth optimization as, for example, observed in the training of neural networks. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/10556788.2024.2414186
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        Text: English
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      – SubjectFull: Nonsmooth optimization
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
      – SubjectFull: Deep learning
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      – SubjectFull: Global optimization
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      – SubjectFull: Cost functions
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      – TitleFull: A piecewise smooth version of the Griewank function.
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              Text: Apr2026
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