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

  • K. I. M. Mckinnon
  • C. Millar
  • M. Mongeau
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

This paper addresses the problem of minimizing the Gibbs free energy in the n c -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 global optimization steps in n-space, and local optimization steps in nK-space, Kn + 1.

We describe an algorithm performing the global optimization step involved in this lower-dimensional search space using techniques from interval analysis. We report good numerical results on instances of the Gibbs free energy minimization problem.

Keywords

Global optimization interval analysis tangent-plane criterion Gibbs free energy chemical and phase equilibrium non-convex optimization 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • K. I. M. Mckinnon
    • 1
    • 2
  • C. Millar
    • 1
    • 2
  • M. Mongeau
    • 1
    • 2
  1. 1.Dept of Mathematics and StatisticsUniversity of EdinburghUK
  2. 2.Labo Approximation & OptimisationUniversité Paul SabatierToulouse cedexFrance

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