The simplex procedure is described by J. A. Nelder and R. Mead in the paper:
A simple method for function minimization, The Computer Journal 7, 308-313 (1965).
It is a nonlinear regression method which requires only the evaluation of the function. No derivatives have to be computed.
The following software books describe the Simplex procedure in details:
D. H. Besset
"Object-oriented implementation of numerical methods. An introduction with Java and Smalltalk", page 558, Morgan Kaufmann, San Francisco (2001).
N. C. Shammas
"Mathematical algorithms in Visual Basic for scientists and engineers", page 118, McGraw-Hill, New York (1996).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannnery
"Numerical recipes in C. The art of scientific computing", 2nd edn., page 408, Cambridge University Press, Cambridge (1992).
K. Ebert, H. Ederer, and T. L. Isenhour
"Computer applications in chemistry. An introduction for PC users", page 387, VCH, New York (1989).
Computerized shimming with the Simplex algorithm (PDF2 file, 334 k) (PDF1 file, 364 k) by William E. Hull.