Geodesic
On the interior point method for solving thermodynamic equilibrium problems
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 69-77

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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. 
@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},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a8/}
}
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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/