MDSMAX  Multidirectional search method for direct search optimization.
        [x, fmax, nf] = MDSMAX(FUN, x0, STOPIT, SAVIT) attempts to
        maximize the function FUN, using the starting vector x0.
        The method of multidirectional search 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).
        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.
        MDSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional
        arguments to be passed to fun, via feval(fun,x,P1,P2,...).

 This implementation uses 2n^2 elements of storage (two simplices), where x0
 is an n-vector.  It is based on the algorithm statement in [2, sec.3],
 modified so as to halve the storage (with a slight loss in readability).

 References:
 [1] V. J. Torczon, Multi-directional search: A direct search algorithm for
     parallel machines, Ph.D. Thesis, Rice University, Houston, Texas, 1989.
 [2] V. J. Torczon, On the convergence of the multidirectional search
     algorithm, SIAM J. Optimization, 1 (1991), pp. 123-145.
 [3] N. J. Higham, Optimization by direct search in matrix computations,
     SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993.
 [4] N. J. Higham, Accuracy and Stability of Numerical Algorithms,
        Second edition, Society for Industrial and Applied Mathematics,
        Philadelphia, PA, 2002; sec. 20.5.

Package: optim