Introduction Solving a nonlinear least squares problem consists of minimizing a least squares objective function made up of residuals \(g_1(\boldsymbol{\theta}), \ldots, g_n(\boldsymbol{\theta})\) that are nonlinear functions of the parameters of interest \(\boldsymbol{\theta} = (\theta_1,\ldots, \theta_p)'\):

Introduction Automatic differentiation Automatic differentiation (AD) refers to the automatic/algorithmic calculation of derivatives of a function defined as a computer program by repeated application of the chain rule. Automatic differentiation plays an important role in many statistical computing problems, such as gradient-based optimization of large-scale models, where gradient calculation by means of numeric differentiation (i.

Introduction The new gslnls-package provides R bindings to nonlinear least-squares optimization with the GNU Scientific Library (GSL) using the trust region methods implemented by the gsl_multifit_nlinear module. The gsl_multifit_nlinear module was added in GSL version 2.