The number, nature and composition of phases at physical equilibrium a
re determined by minimizing Gibbs free energy. The existence of the ph
ases is described by a set of binary variables which lead to the formu
lation of a MINLP problem. The resolution of the initial MINLP problem
leads to the resolution of Non Linear Programming subproblems which c
ontain local extrema. We propose to determine the global optimum of ea
ch NLP problem by the;se of a homotopy continuation method. This origi
nal resolution is illustrated on a L-L-V equilibrium problem.