To understand the structure and content of pars and aux, see the source code of the mlgarch function
Returns
mlgarchObjective returns the log-likelihood of the VARMA representation, whereas mlgarchRecursion1 returns the residuals of the VARMA representation associated with the VARMA parameters pars
References
Sucarrat, Gronneberg and Escribano (2013), 'Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown', MPRA Paper 49344: http://mpra.ub.uni-muenchen.de/49344/