4.2.2 A Levenberg-Marquardt Optimization Tool

To perform optimization on a vector of target quantities, rather than just optimizing a single quantity, SIESTA offers the services of the LMMIN optimization tool. It is an implementation of the Levenberg-Marquardt algorithm. LMMIN is a perfect basis for inverse modeling purposes due to its enhanced features. For example LMMIN allows to specify limits for each of the free parameters used for optimization. Thereby, we can avoid unphysical or at least unreasonable values of parameters during the optimization procedure and thus the risk of running into a local optimum associated with these values is eliminated. Furthermore, we can avoid malfunctions of simulation tools which require their parameters to be within certain ranges for a proper operation. The keywords gradient and tolerance define the step size used for gradient computation and a termination criterion, respectively.