Variable projection for nonlinear least squares problems

The variable projection algorithm of Golub and Pereyra (SIAM J. Numer. Anal. 10:413–432, <CitationRef CitationID="CR12">1973</CitationRef>) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementation of this algorithm, include constraints on the parameters, more clearly identify key ingredients so that improvements can be made, compute the Jacobian matrix more accurately, and make future implementations in other languages easy. Copyright US National Institute of Standards and Technology 2013