The R Journal: article published in 2021, volume 13:2

Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg PDF download
Viviane Philipps, Boris P. Hejblum, Mélanie Prague, Daniel Commenges and Cécile Proust-Lima , The R Journal (2021) 13:2, pages 365-379.

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 con vergence 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 reli ably 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.

Received: 2020-10-30; online 2021-10-19, supplementary material, (16.7 MiB)
CRAN packages: base, optimx, minpack.lm, nlmrt, marqLevAlg, doParallel, foreach, JM, lcmm, optimParallel, optim, roptim, DEoptim, GA, rgenoud, hydroPSO
CRAN Task Views cited directly: Optimization
CRAN Task Views implied by cited CRAN packages: Optimization, HighPerformanceComputing, ChemPhys, Cluster, Hydrology, MachineLearning, Survival

CC BY 4.0
This article and supplementary materials are licensed under a Creative Commons Attribution 4.0 International license.

  author = {Viviane Philipps and Boris P. Hejblum and Mélanie Prague and
          Daniel Commenges and Cécile Proust-Lima},
  title = {{Robust and Efficient Optimization Using a Marquardt-
          Levenberg Algorithm with R Package marqLevAlg}},
  year = {2021},
  journal = {{The R Journal}},
  doi = {10.32614/RJ-2021-089},
  url = {},
  pages = {365--379},
  volume = {13},
  number = {2}