Geodesic
On the interior point method for solving thermodynamic equilibrium problems
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 69-77 
V. P. Il'in; K. G. Morgunov; A. N. Chaiko. On the interior point method for solving thermodynamic equilibrium problems. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 69-77. http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a8/
@article{SJIM_2011_14_2_a8,
     author = {V. P. Il'in and K. G. Morgunov and A. N. Chaiko},
     title = {On the interior point method for solving thermodynamic equilibrium problems},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {69--77},
     year = {2011},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a8/}
}
TY  - JOUR
AU  - V. P. Il'in
AU  - K. G. Morgunov
AU  - A. N. Chaiko
TI  - On the interior point method for solving thermodynamic equilibrium problems
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2011
SP  - 69
EP  - 77
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a8/
LA  - ru
ID  - SJIM_2011_14_2_a8
ER  - 
%0 Journal Article
%A V. P. Il'in
%A K. G. Morgunov
%A A. N. Chaiko
%T On the interior point method for solving thermodynamic equilibrium problems
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2011
%P 69-77
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a8/
%G ru
%F SJIM_2011_14_2_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of thermodynamic equilibrium in multicomponent systems with a given total composition as a traditional inverse problem. We propose a modification of the corresponding optimization problem for which, considering the specifics of the target functional, and basing on the interior point method we develop a two-level iterative process and sos find a solution satisfying the Karush–Kuhn–Tucker conditions. The results of simulations confirm the convergence of the method and demonstrate its wider applicability in comparison with analogous methods.

[1] Belov G. V., Termodinamicheskoe modelirovanie, Nauch. mir, M., 2002

[2] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[3] Fiacco A. V., McCormick G. P., Nonlinear Programming: Unconstrained Minimization Techniques, John Wiley and Sons, N.Y., 1968 | MR | Zbl

[4] Gay D. M., Overton M. L., Wight M. H., “A primal-dual interior method for nonconvex nonlinear programming”, Advances in Nonlinear Programming, Kluver, Dordrecht, 1998, 31–56 | MR | Zbl

[5] Argaez M., Exact and Inexact Newton Linesearch Interior-Point Algorithms for Nonlinear Programming Problems, Rice Univ., Houston, 1997 | MR

[6] Karpov I. K., Chudneneko K. V., Kulik D. A., “Modeling chemical mass transfer in geochemical process: thermodynamic relations, conditions of equilibria, and numerical algorithms”, Amer. J. Sci., 297 (1997), 767–806 | DOI

[7] Borisov M. V., Shvarov Yu. V., Termodinamika geokhimicheskikh protsessov, Izd-vo MGU, M., 1992

[8] Akinfeev N. N., “Algoritm rascheta geterogennykh ravnovesii dlya mikroevm”, Geokhimiya, 1986, no. 6, 882–889

[9] Morgunov K. G., “Baza termodinamicheskikh dannykh i programmnoe obespechenie, prednaznachennoe dlya resheniya zadach postroeniya diagramm mineralnykh ravnovesii”, Vestnik otdeleniya nauk o Zemle RAN, 2004, no. 1, 1–16 http://www.scgis.ru/russian/cp1251/h_dgggms/1-2004/inform-1.pdf

[10] Chaiko A. N., “Minimizatsiya svobodnoi energii v ravnovesnoi termodinamike”, Tr. konf. molodykh uchenykh, izd. IVMiMG SO RAN, Novosibirsk, 2005, 187–195

[11] Karpov I. K., Fiziko-khimicheskoe modelirovanie na EVM v geokhimii, Nauka, Novosibirsk, 1981

[12] Ciavatta L., “The specific interaction theory in evaluating ionic equilibria”, Ann. Chim., 70 (1980), 551–567

[13] Karpov I. K., Kiselev A. I., Letnikov F. A., Khimicheskaya termodinamika v petrologii i geokhimii, Izd-vo SO AN SSSR, Irkutsk, 1971

[14] Johnson J., Oelkers E., Helgeson H., “SUPCRT' 92”, Computer and Geosciences, 18 (1992), 899–947 | DOI