The method of Marquardt's compromise for handling the problem of near-singularity in nonlinear regression is modified by (a) utilizing methods from ridge regression for computing the Marquardt parameter k, and (b) utilizing a search method of interpolation-extrapolation for determining the step size. The performance of these modifications is evaluated on a number of standard test problems from the literature. It is shown that the Lawless-Wang estimate of k without the benefit of interpolation- extrapolation competes favorably with standard algorithms implemented in packaged programs. An application to a model of plasma insulin dynamics is also given. Comparison of the modified procedure with the Nelder-Mead simplex method is given. © 1983.
Garcia-Peña, J., Azen, S. P., & Bergman, R. N. (1983). On a modification of Marquardt’s compromise: Rationale and applications. Applied Mathematics and Computation, 12(1), 1–17. https://doi.org/10.1016/0096-3003(83)90039-5