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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.

*Rudi Strasser *

1999-05-27