Models have been developed allowing adequate description of the behavior of concentrated aqueous solutions. One of them is the well-known Pitzer model proposed for the description of the properties of dense electrolyte solutions in a wide range of temperatures, pressures, and compositions, thus this one requires the knowledge of interaction parameters between particles. Indeed, Pitzer (1973) has developed its model for an electrolyte while introducing a set of interaction parameters whether binary or ternary ones. Hence, the aim of our work is the numerical determination of theses parameters. We have developed an algorithm based on Pitzer equations as well as the Nelder-Mead simplex method, which is an optimization method for multivariate functions, afterward the algorithm has been approved by applying it on the ternary system, of which we already dispose Pitzer parameters as well as its isotherm, we made use of the ternary system Li2SO4+MgSO4+H2O at 208.15°K, this comparison has successfully confirmed the accuracy and the effectiveness of our work.