Himmelblau's function

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(-3.779310, -3.283186) = 0.0 quad, f(-2.805118, 3.131312) = 0.0 quad, f(3.584428, -1.848126) = 0.0 quad, f(3.0, 2.0) = 0.0 quad.

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


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