Optimisation algorithms

Prior to minimisation, all optimisation algorithms require a starting position within the optimisation space. This initial parameter vector is found by employing a coarse grid search - chi-squared values at regular positions spanning the space are calculated and the grid point with the lowest value becomes the starting position. The grid search itself is an optimisation technique. As it is computationally expensive the number of grid points needs to be kept to a minimum. Hence the initial parameter values are a rough and imprecise approximation of the local minimum.

Once the starting position has been determined by the grid search the optimisation algorithm can be executed. The number of algorithms developed within the mathematical field of optimisation is considerable. They can nevertheless be grouped into one of a small number of major categories based on the fundamental principles of the technique. These include the line search methods, the trust region methods, and the conjugate gradient methods. For more details on the algorithms described below see Nocedal and Wright (1999).