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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:

^{[2]}

Its global optimum point is

**^**Ackley, D. H. (1987) "A connectionist machine for genetic hillclimbing", Kluwer Academic Publishers, Boston MA. p. 13-14**^**Bäck, Thomas (1996-02-15). "Artificial Landscapes".*Evolutionary Algorithms in Theory and Practice*. Oxford University Press. p. 142. doi:10.1093/oso/9780195099713.003.0008. ISBN 978-0-19-509971-3.