March 1999

Introduction Nelder and Mead (1965) give a method of minimizing a function of n variables by first computing its value at each of the n+1 points of a simplex defined by an initial point (x 1 , x 2 , ...,x n ) and the n points (x 1 , 0,..., 0), (0, x 2 ,..., 0), ..., (0, 0,..., x n ) . By a sequence of operations called reflections, contractions and expansions the point corresponding to the maximum functional value is successively replaced by a point with a smaller value. This process is repeated until the variance of the functional values over the simplex is smaller than a given tolerance or until a maximum number of cycles is exceeded, whichever occurs first. The present note gives a J program for this algorithm and a Windows form for its convenient use. Windows