Griewank function

First order Griewank function.

In mathematical optimization, the Griewank function is used as a performance test problem for optimization algorithms. For order $n$ it is defined by:

$f(x_{1},x_{2},\ldots ,x_{n}):=1+{\frac {1}{4000}}\sum _{i=1}^{n}x_{i}^{2}-\prod _{i=1}^{n}\cos \left({\frac {x_{i}}{\sqrt {i}}}\right).$

The Griewank function has a global minimum at $f(0,0,\ldots ,0)=0$ and multiple local minima. A typical search area is $x_{i}=[-600,600]$, for $i=1,\ldots ,n$ .

See also

• Test functions for optimization