Himmelblau's function

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Himmelblau's function
In 3D
Log-spaced level curve plot

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 and where , 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.[citation needed]

The function is named after David Mautner Himmelblau (1924–2011), who introduced it.[1]

See also[edit]


  1. ^ Himmelblau, D. (1972). Applied Nonlinear Programming. McGraw-Hill. ISBN 0-07-028921-2.