Comptes Rendus
no. 9
Numerical Analysis
An optimization problem related to the modeling of atmospheric inorganic aerosols
[Un problème d'optimisation lié à la modélisation d'aérosols inorganiques]

Présenté par : Roland Glowinski

Neal R. Amundson1 ; Alexandre Caboussat1 ; Jiwen He1 ; John H. Seinfeld2 ; Kee-Youn Yoo3
1 Department of Mathematics, University of Houston, Houston, TX 77204, USA
2 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
3 Department of Chemical Engineering, Seoul National University of Technology, Seoul 139-743, South Korea
Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 683-686.

Nous proposons un modèle pour l'étude de l'équilibre chimique d'un aérosol inorganique dilué dans l'air. L'état d'équilibre est caracterisé par le minimum d'énergie de Gibbs pour un système chimique faisant intervenir une phase liquide, une phase gazeuse et plusieurs phases solides. Nous présentons une méthode pour la résolution des conditions de Karush–Kuhn–Tucker. Nous utilisons un algorithme de type active set, couplé avec une méthode de Newton pour déterminer le minimum d'énergie ainsi que les phases solides apparaissant à l'équilibre.

A mathematical model for the computation of chemical equilibrium of atmospheric inorganic aerosols is proposed. The equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual method solving the Karush–Kuhn–Tucker conditions is detailed. An active set/Newton method permits the computation of the minimum and track solid salts at the equilibrium.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.01.025
Neal R. Amundson 1 ; Alexandre Caboussat 1 ; Jiwen He 1 ; John H. Seinfeld 2 ; Kee-Youn Yoo 3

1 Department of Mathematics, University of Houston, Houston, TX 77204, USA
2 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
3 Department of Chemical Engineering, Seoul National University of Technology, Seoul 139-743, South Korea 
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     title = {An optimization problem related to the modeling of atmospheric inorganic aerosols},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {683--686},
     publisher = {Elsevier},
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     year = {2005},
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Neal R. Amundson; Alexandre Caboussat; Jiwen He; John H. Seinfeld; Kee-Youn Yoo. An optimization problem related to the modeling of atmospheric inorganic aerosols. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 683-686. doi : 10.1016/j.crma.2005.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.025/

[1] A.S. Ansari; S.N. Pandis Prediction of multicomponent inorganic atmospheric aerosol behavior, Atmospheric Environment, Volume 33 (1999) no. 5, pp. 745-757

[2] P.E. Gill; W. Murray; M.A. Saunders; M.H. Wright Inertia-controlling methods for general quadratic programming, SIAM Rev., Volume 33 (1991) no. 1, pp. 1-36

[3] N.I.M. Gould On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem, Math. Programming, Volume 32 (1985), pp. 90-99

[4] K. Kunisch; F. Rendl An infeasible active set method for quadratic problems with simple bounds, SIAM J. Optim., Volume 14 (2003) no. 1, pp. 35-52

[5] A. Nenes; S.N. Pandis; C. Pilinis Continued development and testing of a new thermodynamic aerosol module for urban and regional air quality models, Atmospheric Environment, Volume 33 (1999) no. 10, pp. 1553-1560

[6] K.-Y. Yoo; J.-W. He; N.R. Amundson Canonical form and mathematical interpretation of electrolyte solution systems, Korean J. Chem. Eng., Volume 21 (2004) no. 2, pp. 303-307

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