The Powell optimization method.
powell [iters] [eps] [tol] [huge]
The POWELL method is a single-shot method which attempts to find the local fit-statistic minimum nearest to the starting point. Its principal advantage is that it is a robust direction-set method. A set of directions (e.g., unit vectors) are defined; the method moves along one direction until a minimum is reached, then from there moves along the next direction until a minimum is reached, and so on, cycling through the whole set of directions until the fit statistic is minimized for a particular iteration. The set of directions is then updated and the algorithm proceeds. Its principal disadvantages are that it will not find the local minimum as quickly as LEVENBERG-MARQUARDT if the statistic surface is well-behaved, and there is no guarantee it will find the global fit-statistic minimum.
The eps parameter controls when the optimization will cease; for POWELL, this will occur when
| S_i - S_(i-1) | < 0.5 * eps * ( |S_i| + |S_(i-1)| )
where S_(i-1) and S_i are the observed statistic values for the (i-1)th and ith iteration, respectively.
Parameter=iters (integer default=2000 min=1 max=10000)
Maximum number of iterations.
Parameter=eps (real default=1.e-6 min=1.e-9 max=0.001)
Criterion to stop fit.
Parameter=tol (real default=1.e-6 min=1.e-8 max=0.1)
Tolerance in lnmnop
Parameter=huge (real default=1.e+10 min=1000 max=1.e+12)
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