Introduction | Methodology | The Marquardt-Levenberg algorithm | Stringent convergence criteria | Derivatives calculation | Special case of a log-likelihood maximization | Implementation | marqLevAlg function | Implementation of parallel computations | Example | Benchmark | Simulated dataset | Statistical models | Joint shared random effect model for a longitudinal marker and a time to event: package JM | Latent class linear mixed model: package lcmm | Multivariate latent process mixed model: package CInLPN | Results | Comparison with other optimization algorithms | Other Marquardt-Levenberg implementations | Examples from the litterature | Example of complex optimization problem: Maximum Likelihood Estimation of a Joint model for longitudinal and time-to-event data | Concluding remarks | Funding | Acknowlegdments | Appendix | A1. Standard examples from the litterature | A2. Marquardt-Levenberg implementations for nonlinear least square problems | A3. Other parallelized optimization algorithms | A4. Sensitivity to initial values | Comparison with another Marquardt-Levenberg implementation | Global optimization using grid search