Nonlinear Mixed effects models are hidden variables models that are widely used in many field such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters such as covariates or correlations which must be selected. Recent development of pharmacogenomics has brought averaged/high dimensional problems to the field of nonlinear mixed effects modeling for which standard covariates selection techniques like stepwise methods are not well suited. This work proposes to select covariates and correlation parameters using a penalized likelihood approach. The penalized likelihood problem is solved using a stochastic proximal gradient algorithm to avoid inner-outer iterations. Speed of convergence of the proximal gradient algorithm is improved by the use of component-wise adaptive gradient step sizes. The practical implementation and tuning of the proximal gradient algorithm is explored using simulations. Calibration of regularization parameters is performed by minimizing the Bayesian Information Criterion using particle swarm optimization, a zero order optimization procedure. The use of warm restart and parallelization allows to reduce significantly computing time. The performance of the proposed method compared to the traditional grid search strategy is explored using simulated data. Finally, an application to real data from two pharmacokinetics studies is provided, one studying an antifibrinolitic and the other studying an antibiotic.
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