Calculation of phase and chemical equilibria is of fundamental importance for the design and simulation of chemical processes. Methods of minimizing the Gibbs free energy provide equilibrium solutions that are candidates only for the true equilibrium solution, because the number and type of phases must be assumed before the Gibbs energy minimization problem can be formulated. The tangent plane stability criterion was used to determine the stability of a candidate equilibrium solution. The Gibbs energy minimization and tangent plane stability problems are challenging due to highly nonlinear thermodynamic functions. This work develops a global optimization approach for the tangent plane stability problem that provides a theoretical guarantee about the stability of the candidate equilibrium solution with computational efficiency. Cubic equations of state were used due to their ability to accurately predict the behavior of nonideal vapor and liquid phases across a broad range of pressures. The mathematical form of the stability problem was analyzed and nonlinear functions with special structure were identified to achieve faster convergence of the algorithm. This approach, when applied to the SRK, Peng-Robinson, and van der Waals cubic equations of state, could address a variety of mixing rules. Computational results on problems with two-eight components are presented.