Finding multiple stationary points of the Gibbs tangent plane distance function via the topographical global initialization

Abstract

In order to find multiple stationary points of the Gibbs tangent plane distance function, often required in the stability analysis used in phase equilibrium calculations, in this article we apply a recently revisited version of the topographical global initialization. This initialization technique is a simple and ingenious approach based on elementary concepts of graph theory. Here, the topographical initialization is employed to generate good starting points to solve a constrained global minimization problem, whose solutions are the roots of a nonlinear system, which describes the first-order stationary conditions associated with the Gibbs plane tangent criterion for phase stability analysis. To accomplish the task of local search, in the minimization step we use a well-established interior-point method. Our methodology was compared against another robust method using benchmarks from the literature. Results indicated that the present approach is a powerful strategy for finding multiple stationary points of the Gibbs tangent plane distance function, having demonstrated high efficiency and robustness.