1.7 A Nelder-Mead simplex algorithm

Helptext:

NMSMAX  Nelder-Mead simplex method for direct search optimization.
       [x, fmax, nf] = NMSMAX(FUN, x0, STOPIT, SAVIT) attempts to
       maximize the function FUN, using the starting vector x0.
       The Nelder-Mead direct search method is used.
       Output arguments:
              x    = vector yielding largest function value found,
              fmax = function value at x,
              nf   = number of function evaluations.
       The iteration is terminated when either
              - the relative size of the simplex is <= STOPIT(1)
                (default 1e-3),
              - STOPIT(2) function evaluations have been performed
                (default inf, i.e., no limit), or
              - a function value equals or exceeds STOPIT(3)
                (default inf, i.e., no test on function values).
       The form of the initial simplex is determined by STOPIT(4):
          STOPIT(4) = 0: regular simplex (sides of equal length, the default)
          STOPIT(4) = 1: right-angled simplex.
       Progress of the iteration is not shown if STOPIT(5) = 0 (default 1).
          STOPIT(6) indicates the direction (ie. minimization or 
                  maximization.) Default is 1, maximization.
                  set STOPIT(6)=-1 for minimization
       If a non-empty fourth parameter string SAVIT is present, then
       `SAVE SAVIT x fmax nf' is executed after each inner iteration.
       NB: x0 can be a matrix.  In the output argument, in SAVIT saves,
           and in function calls, x has the same shape as x0.
       NMSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional
       arguments to be passed to fun, via feval(fun,x,P1,P2,...).
References:
N. J. Higham, Optimization by direct search in matrix computations,
   SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993.
C. T. Kelley, Iterative Methods for Optimization, Society for Industrial
   and Applied Mathematics, Philadelphia, PA, 1999.