The ADMB project supports the application of automatic differentiation (AD) for solutions to non-linear statistical modeling and optimization problems.
AD Model Builder, or ADMB, is a C++ application which implements AD using specialized classes and operator overloading. ADMB can be downloaded from this site. For further information about ADMB, see ADMB citation
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A., and Sibert, J. 2012. AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optim. Methods Softw. 27:233-249.
Template Model Builder, or TMB, is a statistical modeling package which implements AD using C++ templates and is integrated with the R statistical language. TMB can be downloaded from from the TMB github site. For further information about TMB, see the TMB Wiki and the primary publication, see TMB citation
Kristensen, K., Nielsen, A., Berg, C.W., Skaug, H.J., Bell, B. 2016, TMB: Automatic Differentiation and Laplace Approximation.