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

@article{Philipps2021RobustAE,
  title={Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg},
  author={Viviane Philipps and Boris P. Hejblum and M{\'e}lanie Prague and Daniel Commenges and C{\'e}cile Proust-Lima},
  journal={R J.},
  year={2021},
  volume={13},
  pages={273}
}
Optimization is an essential task in many computational problems. In statistical modelling for instance, in the absence of analytical solution, maximum likelihood estimators are often retrieved using iterative optimization algorithms. R software already includes a variety of optimizers from general-purpose optimization algorithms to more specific ones. Among Newton-like methods which have good convergence properties, the Marquardt-Levenberg algorithm (MLA) provides a particularly robust… 

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References

SHOWING 1-10 OF 49 REFERENCES
Genetic Optimization Using Derivatives: The rgenoud Package for R
TLDR
This introduction to the R package rgenoud is a modied version of Mebane and Sekhon (2011), published in the Journal of Statistical Software and contains higher resolution gures.
Unifying Optimization Algorithms to Aid Software System Users: optimx for R
TLDR
This work attempts to provide some diagnostic information about the function, its scaling and parameter bounds, and the solution characteristics of optimx, a wrapper to consolidate many of these choices for the optimization of functions that are mostly smooth with parameters at most bounds-constrained.
A Newton-Like Algorithm for Likelihood Maximization: The Robust-Variance Scoring Algorithm
TLDR
The robust-variance scoring (RVS) algorithm is studied, which replaces minus the Hessian of the loglikelihood used in the Newton-Raphson algorithm by a matrix $G$ which is an estimate of the variance of the score under the true probability, which uses only the individual scores.
Numerical optimization and surface estimation with imprecise function evaluations
TLDR
The present work attempts to classify both problems and algorithmic tools in an effort to prescribe suitable techniques in a variety of situations to minimize functions of several parameters where the function need not be computed precisely.
Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data
Abstract We develop an efficient and effective implementation of the Newton—Raphson (NR) algorithm for estimating the parameters in mixed-effects models for repeated-measures data. We formulate the
A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES
The standard method for solving least squares problems which lead to non-linear normal equations depends upon a reduction of the residuals to linear form by first order Taylor approximations taken
optimParallel: An R Package Providing a Parallel Version of the L-BFGS-B Optimization Method
TLDR
The R package optimParallel provides a parallel version of the L-BFGS-B optimization method of optim(), which has the same usage and output as optim().
Title R interface to the Levenberg-Marquardt nonlinear least-squares algorithm found in MINPACK, plus support for bounds
TLDR
R interface to lmder and lmdif from the MINPACK library, for solving nonlinear least-squares problems by a modification of the Levenberg-Marquardt algorithm.
On Some Extensions to GA Package: Hybrid Optimisation, Parallelisation and Islands EvolutionOn some extensions to GA package: hybrid optimisation, parallelisation and islands evolution
Genetic algorithms are stochastic iterative algorithms in which a population of individuals evolve by emulating the process of biological evolution and natural selection. The R package GA provides a
Continuous Global Optimization in R
TLDR
A new R package globalOptTests is presented that provides a set of standard test problems for continuous global optimization based on C functions by Ali, Khompatraporn, and Zabinsky (2005).
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