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

TL;DR

This paper introduces marqLevAlg, an R package implementing a robust, efficient Marquardt-Levenberg optimization algorithm that improves convergence reliability and reduces computation time in complex local optimization problems.

Contribution

The paper presents a new R package with a Marquardt-Levenberg algorithm that enhances robustness and efficiency in local optimization, addressing limitations of existing methods.

Findings

Reliable convergence to optima even in complex problems

Significant reduction in computational time

Effective prevention of saddle point convergence

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.