MS 95-001 Abstract

Global Optimization for the Chemical and Phase Equilibrium Problem using Interval Analysis

K.I.M. McKinnon, C. Millar and M. Mongeau

Technical Report MS 95-001

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 analysis. We report promising numerical results on instances of the Gibbs free energy minimization problem.

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

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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.
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