An algorithm that may be appropriate when the gradient of 
is hard to calculate, or when the function value
contains noise, is the nonlinear simplex method. For an 
-dimensional problem, this method maintains a simplex of 
points (a triangle in two dimensions,
or a pyramid in three dimensions). The simplex moves, expands, contracts, and distorts its
shape as it attempts to find a minimizer. This method is slow and can be applied only to
problems in which is small. It is, however, extremely popular, since it requires the user to
supply only function values, not derivatives. IMSL , MATLAB , NAG(FORTRAN) , NAG(C) , PORT 3 , and PROC NLP contain implementations of
this method.
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Updated 28 March 1996
