This paper addresses the problem of minimizing the Gibbs free energy in the
n-component, multi-phase chemical and phase equilibrium problem involving
different thermodynamic models. The algorithmic approach used is based on
the tangent-plane criterion of Gibbs: the global optimization problem
considered, which involves a search space of n(n-1) dimensions, is
reduced to a finite sequence of
local optimization steps in K(n-1)-space, K <= n, and
global optimization steps in (n-1)-space.
We describe an algorithm performing the global optimization step involved
in this lower-dimensional search space using techniques from interval
We report good numerical results on instances of the Gibbs free
energy minimization problem.
Global optimization, interval analysis, tangent-plane criterion,
Gibbs free energy, chemical and phase equilibrium, non-convex optimization.
This version was
accepted in March 1995 for the Princeton conference on
global optimization, 1995,
and publised in
"Global optimization" Editors C. Floudas and P.M.Pardalos, Kluwer Academic
Press, pp365-382, 1995.