Himmelblau's function

In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by:

It has one local maximum at ${\displaystyle x=-0.270845\,}$ and ${\displaystyle y=-0.923039\,}$ where ${\displaystyle f(x,y)=181.617\,}$, and four identical local minima:

The locations of all the minima can be found analytically. However, because they are roots of cubic polynomials, when written in terms of radicals, the expressions are somewhat complicated.

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