Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg

Authors

Viviane Philipps, Bordeaux Population Health Research Center
Boris P. Hejblum, Bordeaux Population Health Research Center
Mélanie Prague, Bordeaux Population Health Research Center
Daniel Commenges, Bordeaux Population Health Research Center
Cécile Proust-Lima, Bordeaux Population Health Research Center

Date of this Version

12-2021

Document Type

Article

Citation

The R Journal (December 2021) 13(2); Editor: Dianne Cook

Comments

Copyright 2021, The R Foundation. Open access material. License: CC BY 4.0 International

Abstract

Implementations in R of classical general-purpose algorithms for local optimization generally have two major limitations which cause difficulties in applications to complex problems: too loose convergence criteria and too long calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a Newton-like method particularly robust for solving local optimization problems, we provide with marqLevAlg package an efficient and general-purpose local optimizer which (i) prevents convergence to saddle points by using a stringent convergence criterion based on the relative distance to minimum/maximum in addition to the stability of the parameters and of the objective function; and (ii) reduces the computation time in complex settings by allowing parallel calculations at each iteration. We demonstrate through a variety of cases from the literature that our implementation reliably and consistently reaches the optimum (even when other optimizers fail) and also largely reduces computational time in complex settings through the example of maximum likelihood estimation of different sophisticated statistical models.