Publication: A piecewise smooth version of the Griewank function
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A piecewise smooth version of the Griewank function

- Article in a journal -
 

Area
Optimization

Author(s)
Torsten F. Bosse , H. Martin Bücker

Published in
Optimization Methods and Software

Year
2024

Publisher
Taylor & Francis

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.

AD Theory and Techniques
Piecewise Linear

BibTeX
@ARTICLE{
         Bosse2024Aps,
       author = "Torsten F. Bosse and H. Martin Buecker",
       title = "A piecewise smooth version of the Griewank function",
       journal = "Optimization Methods and Software",
       volume = "0",
       number = "0",
       pages = "1--11",
       year = "2024",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2024.2414186",
       url = "https://doi.org/10.1080/10556788.2024.2414186",
       eprint = "https://doi.org/10.1080/10556788.2024.2414186",
       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.",
       ad_area = "Optimization",
       ad_theotech = "Piecewise Linear"
}


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