The Gibbs tangent plane analysis is the crucial method for the determination of the global phase stability and the true equilibrium compositions of the system at elevated pressures. Previous approaches have focused on finding stationary points of the tangent plane distance function (TPDF) described by the cubic equation of state. However, there is no complete guarantee of obtaining all stationary points due to the nonconvex and nonlinear nature of the models used to predict high pressure phase equilibria. After analyzing and reformulating the structure of the derivative function of the TPDF described by the Soave-Redlich-Kwong (SRK) equation of state, it was demonstrated that the Lipschitz constant of the TPDF can be obtained with the calculation precision satisfied. Then the phase stability problem can be solved with E-global convergence. The calculation results for two examples state that the Lipschitz optimization algorithm, i.e., Piyavskii's univariate Lipschitz optimization algorithm used in this paper, can obtain the global minimum of the TPDF for binary mixtures at elevated pressures with complete reliability.