Thermodynamically Consistent Quasi-Newton Formulae

Newton and quasi-Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton-based fixed-point methods have been used to solve many different kinds of chemical process design and optimization problems, perhaps the point of single largest application has been that of multicomponent separation problems, especially equilibrium stage distillation. Quite aside from this, classical thermodynamics provides us with certain fundamental mathematical and physical relationships governing the behavior of nonideal solutions, those being the homogeneity of partial molar excess properties and their derivatives and the Cibbs-Duhem equation. In this work, we draw a connection between the class of Newton-based fixed-