The method of maximum likelihood leads to an ill-posed optimization problem in the case of a mixture of normal distributions. Estimation in the univariate case is reformulated using simple constraints into an optimization problem having a strongly consistent, global solution.
"A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions." Ann. Statist. 13 (2) 795 - 800, June, 1985. https://doi.org/10.1214/aos/1176349557