Dispersion parameter optimisation

For a description of gradients and Hessians, see Section 14.3.2 on page  and Section 14.3.3 on page  respectively. The relaxation dispersion model gradients or Hessians have have either not been calculated for the analytic models or cannot be calculated as the solution is not analytic. Numeric gradients and Hessians could be calculated but this is too computationally expensive, especially for the numeric models where this adds a second layer of numeric approximation.

Optimisation in relax is via the minfx package https://sourceforge.net/projects/minfx/. This allows the Nelder-Mead simplex optimisation technique (see Section 14.4.5 on page ) and the log-barrier constraint algorithm (see Section 14.5.2 on page ) to be used. The advantage of these two techniques is that it enables extremely reliable and high precision optimisation without the use of gradients or Hessians, hence can significantly increase optimisation speeds. They however do not avoid the multiple local minimum problem present in the MMQ models - for that a highly accurate grid search is a reasonable solution.