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The Levenberg-Marquardt algorithm [73] is an efficient method to solve nonlinear least squares problems, and is therefore well suited for inverse modeling tasks. SIESTA provides an interface to the implementation found in the MINPACK [81,82] project.
The parameter values are chosen from prescribed intervals. However, arbitrary constraints are not supported by this optimizer. The step size used for the gradient computation and a tolerance value acting as termination criterion can be adjusted.