Formula omitted]-phase stability testing using the Branch and Bound strategy and the convex-concave splitting of the Helmholtz free energy density

Abstract

We have developed a robust algorithm for the phase stability testing at constant temperature, volume, and moles (specification VTN). The algorithm is based on the convex-concave splitting of the Helmholtz free energy density function and the Branch and Bound strategy. The algorithm uses the Newton-Raphson method with line-search and modified Cholesky decomposition of the Hessian matrix for the local minimization and the Barrier method for the convex underestimate optimization. As our optimization method is global, the special strategy for the initialization of standard local methods is avoided. The performance of the algorithm is demonstrated on several examples of different complexity.