This paper deals with the numerical solution of a difficult class of problems that arise in chemical and phase equilibria. These problems involve the minimization of the Gibbs free energy subject to linear constraints. These constraints represent mass conservation conditions. The approach studied in this paper involves the use of quasi-Newton update methods of minimum norm. The minimum norm updates are used because they provide a least-squares solution to the secant equation. In developing these updates, the method also exploits the structure of the Gibbs free energy function.

In summary, this paper provides a class of robust numerical methods for a difficult and important class of equilibria calculations.