In mathematics, the Griewank function is often used in testing of optimization. It is defined as follows:[1]
First order Griewank function
![{\displaystyle 1+{\frac {1}{4000}}\sum _{i=1}^{n}x_{i}^{2}-\prod _{i=1}^{n}\cos \left({\frac {x_{i}}{\sqrt {i}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/636a078b20d38802f4236ef1839eb3f521cbfa2f)
The following paragraphs display the special cases of first, second and third order
Griewank function, and their plots.
First-order Griewank function
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The first order Griewank function has multiple maxima and minima.[2]
Let the derivative of Griewank function be zero:
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Find its roots in the interval [−100..100] by means of numerical method,
In the interval [−10000,10000], the Griewank function has 6365 critical points.
Second-order Griewank function
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2nd order Griewank function 3D plot
2nd-order Griewank function contour plot
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Third order Griewank function
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Third-order Griewank function Maple animation
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- ^ Griewank, A. O. "Generalized Descent for Global Optimization." J. Opt. Th. Appl. 34, 11–39, 1981
- ^ Locatelli, M. "A Note on the Griewank Test Function." J. Global Opt. 25, 169–174, 2003