This paper deals with the numerical convergence of a cyclic iterative optimization algorithm (CA algorithm) recently developed for maximum likelihood estimation of the parameters of a multinomial model used in road safety modelling. We compare the CA algorithm to some classical constrained optimization algorithms as Nelder–Mead's (NM), Broyden–Fletcher–Goldfarb-Shanno's (BFGS) and Conjugate Gradient (CG). Road accident data is simulated afterwards each of the compared method is applied. In addition to the estimates of the parameters, some useful information as the mean squares error have been computed. The results obtained, for an overall fifty-four thousand (54 000) simulations, show that the CA algorithm is more efficient not only as far as the accuracy is concerned but also and most importantly it is upto 1300 times quicker than the three others.