In
mathematical optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
, 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 polynomial
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d
where the coefficients , , , and are complex numbers, and the variable takes real values, and a\neq 0. In other words, it is both a polynomial function of degree ...
s, when written in terms of radicals, the expressions are somewhat complicated.
The function is named after
David Mautner Himmelblau (1924–2011), who introduced it.
See also
*
Test functions for optimization
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as:
* Convergence rate.
* Precision.
* Robustness.
* General performance.
Here some test functions are ...
References
Mathematical optimization
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