Description

This algorithm provides a numerical solution to the problem of unconstrained local minimization/maximization. This is more efficient than the Gauss-Newton-like algorithm when starting from points very far from the final minimum/maximum. A new convergence test is implemented (RDM) in addition to the usual stopping criterion : stopping rule is when the gradients are small enough in the parameters metric (GH^-1G).

Details

This algorithm provides a numerical solution to the problem of optimizing a function. This is more efficient than the Gauss-Newton-like algorithm when starting from points very far from the final maximum. A new convergence test is implemented (RDM) in addition to the usual stopping criterion : stopping rule is when the gradients are small enough in the parameters metric (GH-1G).

Author(s)

Viviane Philipps, Cecile Proust-Lima, Boris Hejblum, Melanie Prague, Daniel Commenges, Amadou Diakite

References

marqLevAlg Algorithm

Philipps V. Hejblum B.P. Prague M. Commenge D. Proust-Lima C. Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg

Donald W. marquardt An algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2. (Jun, 1963), pp. 431-441.

Convergence criteria : Relative distance to Maximum

Commenges D. Jacqmin-Gadda H. Proust C. Guedj J. A Newton-like algorithm for likelihood maximization : the robust-variance scoring algorithm arxiv:math/0610402v2 (2006)