Linear constraints for the frame order models

Linear constraints are implemented for the frame order models using the log-barrier constraint algorithm in minfx, as this does not require the derivation of gradients.

The pivot point and average domain position parameter constraints in Ångstrom are:

These translation parameter restrictions are simply to stop the optimisation in the case of model failures.
Converting these to the
*A*⋅*x* *b* matrix notation required for the optimisation constraint algorithm, the constraints become

⋅ | (12.80) |

For the order or motional amplitude parameters of the set , the constraints used are

These reflect the range of validity of these parameters.
Converting to the
*A*⋅*x* *b* notation, the constraints are

⋅ | (12.82) |

The pseudo-elliptic cone model constraint
*θ*_{x} *θ*_{y} is used to simplify the optimisation space by eliminating symmetry.

The relax user manual (PDF), created 2020-08-26.