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 promising 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.
Submitted in Jan 1995 for presentation at Princeton conference on
global optimization, 1995.
Revised version MS 95-001a accepted in March 1995 for conference
and publised in
"Global optimization" Editors C. Floudas and P.M.Pardalos, Kluwer Academic
Press, pp365-382, 1995.