Abstract
This paper addresses the problem of minimizing the Gibbs free energy in the
c-component, multi-phase chemical and phase equilibrium problem.
After surveying
previous work in the field and pointing out the main issues in the chemical
and phase equilibrium problem, we extend the
necessary and sufficient condition for global optimality
based on the ``reaction tangent-plane criterion'', to the
case involving different thermodynamical models.
We then present an algorithmic approach that reduces this global
optimization problem (involving a search space of
c(c-1) dimensions) to a finite sequence of local
optimization steps in K(c - 1)-space, K <= m+1 <= c,
and global optimization steps in (c-1)-space (where m is the
number of chemical elements, in the chemical equilibrium problem,
or is equal to c - 1, in the case of the phase equilibrium problem).
The global (phase stability) step uses the tangent-plane criterion
to determine whether the current
solution is optimal, and, if it is not, it finds an improved feasible
solution either with the same number of phases or with one added phase.
The global step also determines what type of phase (e.g. the state;
liquid, vapour) is to be added, if any phase is to be added.
The algorithm is proved to converge to a global minimum in a finite number
of the above local and global steps.

Key words
Global optimization, Gibbs free energy, chemical and phase equilibrium,
non-convex optimization, tangent-plane criterion, convexity.