Nelder-Mead algorithm

The Nelder-Mead simplex algorithm finds a minimum of a function of several variables without differentiation. It is widely used, even though too little is known about its convergence properties. See Nelder, J.A. and Mead, R., "A Simplex Method for Function Minimization", Computer Journal, Vol. 7, Issue 4 (1965), 308-313 for the original article, and see Lagarias, Jeffrey C., James A. Reeds, Margaret H. Wright, and Paul E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal on Optimization, Vol. 9, No. 1 (1998), 112-147.for a more contemporary view of the algorithm. A Google Scholar (scholar.google.com) search on "Nelder-Mead" will demonstrate the level of current activity investigating this algorithm. The Nelder-Mead algorithm is one of those great ideas that turns out to be widely effective and very difficult to analyze mathematically. To begin, we need a definition.