The Rastrigin function is a nonconvex test function used in global optimization theory. In 
dimensions, its usual form is
![f(x)=Ad+sum_(i=1)^d[x_i^2-Acos(2pix_i)],](/images/equations/RastriginFunction/NumberedEquation1.svg) |
where 
is conventional. It has global minimum 
and many regularly spaced local minima produced by the
cosine terms.
The separability and large number of local minima make the function a common benchmark for comparing global optimization algorithms.
Benchmark domains are often restricted to a box such as ![[-5.12,5.12]^d](/images/equations/RastriginFunction/Inline4.svg)
, but the formula itself is defined on all of
.
