Software
Nelder-Mead Simplex Method
We have implemented several versions of the Nelder-Mead Simplex Method. It was originally written it in C, crosen.c, and then ported to FORTRAN 77, frosen.f and FORTRAN 90, frosen.90. The C and FORTRAN 77 versions compile with gcc and g77 respectively. The FORTRAN 90 version compiles with ELF90.
The programs have all been tested with Rosenbrock's function starting at -1.2,1.0 and converge after 54 iterations and 107 function evaluations. In each case the initial simplex is constructed as a regular simplex, as opposed to taking a particular step in the n coordinate directions from the starting point.
Creating the initial simplex in this way means that it will typically have to be scaled. However, we've found that we get better results, at least in out applications - Impedance matching, Optimization of antenna arrays.
nmlatest.c contains the Nelder-Mead algorithm as specified in Margaret H. Wright's paper on Direct Search Methods. It was tested with Rosenbrock's function, as before, with a starting point of -1.2,1.0 and converged after 53 iterations and 105 function evaluations.