A dual extremum principle in thermodynamics

AIChE Journal

Volumn 53, Issue 8, 2007, Pages 2131-2147

  Mitsos, Alexander ^a   Barton, Paul I ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Duality; Extremum principle; Gibbs tangent plane; Lagrangian; Phase equilibrium

Indexed keywords

EXTREMUM PRINCIPLE; GIBBS TANGENT PLANE; LAGRANGIAN METHODS;

GIBBS FREE ENERGY; MIXTURES; PHASE SEPARATION;

PHASE EQUILIBRIA;

GIBBS FREE ENERGY; MIXTURES; PHASE EQUILIBRIA; PHASE SEPARATION;

EID: 34547678026     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.11230     Document Type: Article

References (27)

1. Baker LE, Pierce AC, Luks KD. Gibbs energy analysis of phase equilibria. Soc Petrol Eng J. 1982;22:731-742.
2. Bertsekas DP. Nonlinear Programming, 2nd ed. Belmont, MA: Athena Scientific, 1999.
3. Bertsimas D, Tsitsiklis JN. Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997.
4. Tester JW, Modell M. Thermodynamics and Its Applications, 3rd ed. New Jersey: Prentice Hall, 1997. Prentice Hall International Series in the Physical and Chemical Engineering Sciences.
5. Feinberg M. On Gibbs' phase rule. Arch Rational Mech Anal. 1979;70:219-234.
6. Noll W. On certain convex sets of measures and on phases of reacting mixtures. Arch Rational Mech Anal. 1970;38:1-12.
7. Mistura I. Solutions of the Gibbs-Duhem equation. J Phys A Math Gen. 1979;12:1547-1562.
8. Rabier PJ, Griewank A. Generic aspects of convexification with applications to thermodynamic equilibrium. Arch Rational Mech Anal. 1992;118:349-397.
9. Gutierrez G. Gibbs' phase rule revisited. Theor Math Phys. 1996;108:1222-1224.
10. Michelsen ML. The isothermal flash problem. 1. Stability. Fluid Phase Equilibria. 1982;9:1-19.
11. Michelsen ML. The isothermal flash problem. 2. Phase-split calculation. Fluid Phase Equilibria. 1982;9:21-40.
12. Mcdonald CM, Floudas CA. Global optimization for the phase-stability problem. AIChE J. 1995;41:1798-1814.
13. Blankenship JW, Falk JE. Infinitely constrained optimization problems. J Optim Theory Appl. 1976;19:261-281.
14. Falk JE, Hoffman K. A nonconvex max-min problem. Naval Res Logistics. 1977;24:441-450.
15. Maranas CD, Floudas CA. Finding all solutions of nonlinearly constrained systems of equations. J Global Optim. 1995;7:143-182.
16. Tawarmalani M, Sahinidis NV. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Nonconvex Optimization and its Applications. Boston: Kluwer Academic, 2002.
17. Mcdonald CM, Floudas CA. Decomposition based and branch-andbound global optimization approaches for the phase-equilibrium problem. J Global Optim. 1994;5:205-251.
18. McDonald C, Floudas CA. Global optimization and analysis for the Gibbs free-energy function using the UNTFAC, Wilson, and ASOG equations, Ind Eng Chem Res. 1995;34:1674-1687.
19. Floudas CA, Visweswaran V. A Global optimization algorithm (GOP) for certain classes of nonconvex NLPs. 1. Theory. Comput Chem Eng. 1990;14:1397-1417.
20. Visweswaran V, Floudas CA. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs. 2. Application of theory and test problems. Comput Chem Eng. 1990;14:1419-1434.
21. Floudas CA, Visweswaran V. Primal-relaxed dual global optimization approach. J Optim Theory Appl. 1993;78:187-225.
22. Brooke A, Kendrick D, Meeraus A. GAMS: A User's Guide. Redwood City, CA: The Scientific Press, 1988.
23. Smith JV, Missen RW, Smith WR. General optimality criteria for multiphase multireaction chemical-equilibrium. AIChE J. 1993;39: 707-710.
24. Sieniutycz S, Farkas H, editors. Variational and Extremum Principles in Macroscopic Systems. Oxford: Elsevier, 2005.
25. Baier R, Gerdts M. Intensive course on set-valued numerical analysis and optimal control. http://www.math.uni-hamburg.de/home/ gerdts/TEACHING/ num_analysis_opt_control.pdf 2005.
26. Fosdick R, Patino J. On the Gibbsian thermostatics of mixtures. Arch Rational Mech Anal. 1986;93:203-221.
27. Bank B, Guddat J, Klatte D, Kummer B, Tammer K. Non-Linear Parametric Optimization. Stuttgart: Birkhäuser Verlag, 1983.