Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols |
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| Authors: | N R Amundson A Caboussat J W He J H Seinfeld |
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| Institution: | (1) Department of Mathematics, University of Houston, Houston, Texas, USA;(2) Department of Mathematics, University of Houston, Houston, Texas, USA;(3) Department of Mathematics, University of Houston, Houston, Texas, USA;(4) Department of Chemical Engineering, California Institute of Technology, Pasadena, California, USA |
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| Abstract: | A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is presented. The phase equilibrium is given by the global minimum of the Gibbs free energy for a system that involves water and organic components. This minimization problem is equivalent to the determination of the convex hull of the corresponding molar Gibbs free energy function. A geometrical notion of phase simplex related to the convex hull is introduced to characterize mathematically the phases at equilibrium. A primal-dual interior-point algorithm for the efficient solution of the phase equilibrium problem is presented. A novel initialization of the algorithm, based on the properties of the phase simplex, is proposed to ensure the convergence to a global minimum of the Gibbs free energy. For a finite termination of the interior-point method, an active phase identification procedure is incorporated. Numerical results show the robustness and efficiency of the approach for the prediction of liquid-liquid equilibrium in multicomponent mixtures.Communicated by R. GlowinskiThis work was supported by US Environmental Protection Grant X-83234201. The second author was partially supported by Swiss National Science Foundation Grant PBEL2-103152. |
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| Keywords: | Phase equilibrium problem minimization of Gibbs free energy convex hull phase simplex primal-dual formulation interior-point method |
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