A method introduced by Nelder and Roger Mead in a 1965 paper for finding the maximum (or minimum) of a function. The method begins by evaluating the function at k+1 vertices of a simplex in k dimensions, where k is the number of variables. Subsequent locations are selected automatically, using simple geometric patterns that allow for both the extension of the search area (when, apparently, far from the maximum) and contraction (when close to the maximum). See also response surface.