Himmelblau's function

Plot of Himmelblau's function.

In mathematical optimization, the Himmelblau's 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 one local maximum at $x=-0.270844\quad$ and $y=-0.923038\quad$ where $f(x,y)=181.616\quad$, and four identical local minimums: $f(3.0,2.0)=0.0\quad$,

$f(-2.805118,3.131312)=0.0\quad$,

$f(-3.779310,-3.283186)=0.0\quad$,

$f(3.584428,-1.848126)=0.0\quad$.

The locations of all the minima can be found analytically, but the expressions are long and complicated.

See also

• Rosenbrock function