### 1.10 An alternating directions algorithm

#### Helptext:

    ADSMAX  Alternating directions method for direct search optimization.
           [x, fmax, nf] = ADSMAX(FUN, x0, STOPIT, SAVIT, P) attempts to
           maximize the function FUN, using the starting vector x0.
           The alternating directions 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 increase in function value between successive
                    iterations 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).
           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.
           By default, the search directions are the co-ordinate directions.
           The columns of a fifth parameter matrix P specify alternative search
           directions (P = EYE is the default).
           NB: x0 can be a matrix.  In the output argument, in SAVIT saves,
               and in function calls, x has the same shape as x0.
           ADSMAX(fun, x0, STOPIT, SAVIT, P, P1, P2,...) allows additional
           arguments to be passed to fun, via feval(fun,x,P1,P2,...).
        Reference:
        N. J. Higham, Optimization by direct search in matrix computations,
           SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993.
        N. J. Higham, Accuracy and Stability of Numerical Algorithms,
           Second edition, Society for Industrial and Applied Mathematics,
           Philadelphia, PA, 2002; sec. 20.5.