Himmelblau's function

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Plot of Himmelblau function.

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

$f(x, y) = (x^2+y-11)^2 + (x+y^2-7)^2 \quad$

It has a global minimum at $x=3 \quad$ and $y=2 \quad$ where $f(x, y)=0 \quad$ , and the following local minima: $f(-3.78, -3.28)=0.0054 \quad$ , $f(-2.81, 3.13)=0.0085 \quad$ , $f(3.58, -1.85)=0.0011 \quad$ .