## 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 Ax 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 Ax b notation, the constraints are

 ⋅ (12.82)

The pseudo-elliptic cone model constraint θx θy is used to simplify the optimisation space by eliminating symmetry.

The relax user manual (PDF), created 2016-10-28.