In mathematical optimization, the Ackley function is a non-convex function used as a performance test problem for optimization algorithms. It was proposed by David Ackley in his 1987 PhD dissertation.[1] The function is commonly used as a minimization function with global minimum value 0 at 0,.., 0 in the form due to Thomas Bäck. While Ackley gives the function as an example of "fine-textured broadly unimodal space" his thesis does not actually use the function as a test.
On a 2-dimensional domain it is defined by:
\begin{align} f(x,y)=-20&{}\exp\left[-0.2\sqrt{0.5(x2+y2)}\right]\\ &{}-\exp\left[0.5\left(\cos2\pix+\cos2\piy\right)\right]+e+20 \end{align}
Its global optimum point is
f(0,0)=0.