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<h3 class="section">1.9 An alternating directions algorithm</h3>
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<h4 class="subheading">Helptext:</h4>
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<pre class="verbatim">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.
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