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=== Termination tests ===

	A practical implementation of the Nelder-Mead method must include
a test that ensures termination in a finite amount of time.
The termination test is often composed of three different parts:
<math>\textit{term\_x}\ ,</math> <math>\textit{term\_f}</math> and <math>{\it fail}\ .</math>
* <math>\textit{term\_x}</math> is the ''domain'' convergence or termination test. It becomes ''true'' when the working simplex <math>S</math> is sufficiently ''small'' in some sense (some or all vertices <math>x_j</math> are close enough).
* <math>\textit{term\_f}</math> is the ''function-value'' convergence test. It becomes ''true'' when (some or all) function values <math>f_j</math> are ''close'' enough in some sense.
* <math>{\it fail}</math> is the ''no-convergence'' test. It becomes ''true'' if the number of iterations or function evaluations exceeds some prescribed maximum allowed value.
The algorithm terminates as soon as at least one of these tests becomes ''true''.

	Various forms of <math>\textit{term\_x}</math> and <math>\textit{term\_f}</math> tests have
been used in practice, and some common implementations of the algorithm
have only one of these two tests
(see Singer and Singer, 2001, and Singer and Singer, 2004, for a survey).

	If the algorithm is expected to work for discontinuous functions <math>f\ ,</math>
then it must have some form of a <math>\textit{term\_x}</math> test.
This test is also useful for continuous functions, when a reasonably accurate
minimizing point is required, in addition to the minimal function value.
In such cases, a <math>\textit{term\_f}</math> test is only a safeguard for &ldquo;flat&rdquo;
functions.