In 1965, John Nelder and Roger Mead published an algorithm that has become somewhat famous. MATLAB's fminsearch( ) is based on it; so is Mathematica's NMinimize[ ]. See MathWorld for an outline of the technique. The original paper is:
Nelder, John A. and Mead, Roger (1965, Jan.), "A Simplex Method for Function Minimization", Computer Journal 7 (4): 308-313.
The full text of the paper itself was once available in the form of huge TIFF files at Oxford University Press page; however, at 2007-03-08 the files are unavailable. The paper was published in volume 7, issue 4 of the journal; some citations (such as the one at CiteSeer) omit the issue number.
A contemporary view of the algorithm is provided in this paper:
Lagarias, Jeffrey C., James A. Reeds, Margaret H. Wright, and Paul E. Wright (1998), "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal on Optimization 9 (1): 112-147.
Charles - links
2014-08-18 01:06 EDT