The optimisation space

The optimisation of the parameters of an arbitrary model is dependent on a function *f* which takes the current parameter values
*θ*∈^{n} and returns a single real value
*f* (*θ*)∈ corresponding to position *θ* in the *n*-dimensional space.
For it is that single value which is minimised as

= argf (θ), |
(14.1) |

where
is the parameter vector which is equal to the argument which minimises the function *f* (*θ*).
In most analyses in relax, *f* (*θ*) is the chi-squared equation

where *i* is the summation index over all data, *y*_{i} is the experimental data,
*y*_{i}(*θ*) is the back calculated data, and *σ*_{i} is the experimental error.

The relax user manual (PDF), created 2024-06-08.