Description

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.