# Ackley function

Ackley function of two variables
Contour surfaces of Ackley's function in 3D

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]

On a 2-dimensional domain it is defined by:

{\displaystyle {\begin{aligned}f(x,y)=-20&{}\exp \left[-0.2{\sqrt {0.5(x^{2}+y^{2})}}\,\right]\\&{}-\exp \left[0.5\left(\cos 2\pi x+\cos 2\pi y\right)\right]+e+20\end{aligned}}}

Its global optimum point is

${\displaystyle f(0,0)=0.}$