The number, nature and composition of phases at physical equilibrium are determined by minimizing Gibbs free energy. The existence of the phases is described by a set of binary variables which lead to the formulation of a MINLP problem. The resolution of the initial MINLP problem leads to the resolution of Non Linear Programming subproblems which contain local extrema. We propose to determine the global optimum of each NLP problem by the;se of a homotopy continuation method. This original resolution is illustrated on a L-L-V equilibrium problem.