A regional convexity test for global optimization Application to the phase equilibrium problem

This paper introduces a new method for testing the convexity of a function in an n-rectangular region of its domain which may be used in conjunction with a branch and bound global optimization algorithm to improve its convergence rate. The method makes use of interval analysis techniques together with a determinant test based on Schur complements. Its enhancement of a global optimization algorithm is demonstrated on a set of phase equilibrium problems which are formulated as nonconvex Gibbs energy minimization problems where the Gibbs energy function is modelled using the NRTL equation.