nelder_mead_min (optim_doc)

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### 1.11 Another Nelder-Mead algorithm

This function does gradient-less minimization using the Nelder-Mead algorithm. No constraints are honoured.

#### Helptext:

    [x0,v,nev] = nelder_mead_min (f,args,ctl) - Nelder-Mead minimization

    Minimize 'f' using the Nelder-Mead algorithm. This function is inspired
    from the that found in the book "Numerical Recipes".

    ARGUMENTS
    ---------
    f     : string : Name of function. Must return a real value
    args  : list   : Arguments passed to f.
         or matrix : f's only argument
    ctl   : vector : (Optional) Control variables, described below
         or struct

    RETURNED VALUES
    ---------------
    x0  : matrix   : Local minimum of f
    v   : real     : Value of f in x0
    nev : number   : Number of function evaluations

    CONTROL VARIABLE : (optional) may be named arguments (i.e. "name",value
    ------------------ pairs), a struct, or a vector of length <= 6, where
                       NaN's are ignored. Default values are written <value>.
     OPT.   VECTOR
     NAME    POS
    ftol,f  N/A    : Stopping criterion : stop search when values at simplex
                     vertices are all alike, as tested by

                      f > (max_i (f_i) - min_i (f_i)) /max(max(|f_i|),1)

                     where f_i are the values of f at the vertices.  <10*eps>

    rtol,r  N/A    : Stop search when biggest radius of simplex, using
                     infinity-norm, is small, as tested by :

                 ctl(2) > Radius                                     <10*eps>

    vtol,v  N/A    : Stop search when volume of simplex is small, tested by

                 ctl(2) > Vol

    crit,c ctl(1)  : Set one stopping criterion, 'ftol' (c=1), 'rtol' (c=2)
                     or 'vtol' (c=3) to the value of the 'tol' option.    <1>

    tol, t ctl(2)  : Threshold in termination test chosen by 'crit'  <10*eps>

    narg  ctl(3)  : Position of the minimized argument in args            <1>
    maxev ctl(4)  : Maximum number of function evaluations. This number <inf>
                    may be slightly exceeded.
    isz   ctl(5)  : Size of initial simplex, which is :                   <1>

                   { x + e_i | i in 0..N }

                   Where x == args{narg} is the initial value
                    e_0    == zeros (size (x)),
                    e_i(j) == 0 if j != i and e_i(i) == ctl(5)
                    e_i    has same size as x

                   Set ctl(5) to the distance you expect between the starting
                   point and the minimum.

    rst   ctl(6)   : When a minimum is found the algorithm restarts next to
                     it until the minimum does not improve anymore. ctl(6) is
                     the maximum number of restarts. Set ctl(6) to zero if
                     you know the function is well-behaved or if you don't
                     mind not getting a true minimum.                     <0>

    verbose, v     Be more or less verbose (quiet=0)                      <0>

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