Optimisation de procédés chimiques par une méthode de gradient réduit partie I. Présentation de l'algorithme

 Access to full text

 Full (PDF)

1. 1. J. ABADIE, The GRG Method for Nonlinear Programming, Design and Implementation of Optimization Software, Harvey Greenberg Sijthoff and Noordhof Ed., 1978. 
2. 2. J. ABADIE et J. GUIGOU, Gradient Réduit Généralisé, note HI 069/02, EDF, Clamart, France, 1969. 
3. 3. M. M. ABBOTT et M. C. VAN NESS, Théorie et applications de la thermodynamique, série Schaum, 1978. 
4. 4. R. ARIS, R. BELLMAN et A. KALABA, Some Optimization Problems in Chemical Engineering, C.E.P. Symposium Series, 56, 1960, p. 95. 
5. 5. R. H. BARTELS et G. H. GOLUB, The Simplex Method of Linear Programming Using LU Decomposition, Communications of the A.C.M., 12, 1969, p. 266. Zbl0181.19104
6. 6. J. E. DENNIS et J. J. MORE, Quasi Newton Methods, Motivation and Theory, S.I.A.M. Rev., 19, 1977, p. 46. Zbl0356.65041MR445812
7. 7. S. DOMENECH, Optimisation d'une opération de rectification discontinue - Commande en temps minimal, Thèse de Doctorat d'État, I.N.P., Toulouse, 1976. 
8. 8. S. DOMENECH et M. ENJALBERT, Optimisation d'une opération de rectification discontinue par programmation dynamique, An. Quimi. Real Soc. Esp. Fis. Quim., 74, 1978, p. 319. 
9. 9. S. DOMENECH, G. MURATET et N. THERIENRecherche de commandes optimales liées à l'alimentation d'une usine de traitement d'eaux usées, Tribune du Cebedeau, 31, 1978, p. 241. 
10. 10. E. DURAND, Solutions numériques des équations algébriques, Tome II, Masson et Cie, Paris, 1972. Zbl0099.10801
11. 11. R. FLETCHER et M. J. D. POWELL, On the Modification of LDLT Factorizations, Math. Comp., 28, 1974, p. 1067. Zbl0293.65018MR359297
12. 12. J. J. FORREST et J. A. TOMLIN, Updated Triangular Factors of the Basis to Maintain Sparsity in the Product Form for Simplex Method, Math. Prog., 2, 1972, p. 263. Zbl0288.90048MR307692
13. 13. P. E. GILL, G. H. GOLUB, W. MURRAY et M. A. SAUNDERS, Methods for Modifying Matrix Factorizations, Math. Comp., 28, 1974, p. 505. Zbl0289.65021MR343558
14. 14. P. E. GILL et W. MURRAY, Numerical Methods for Constrained Optimization, Academic Press, 1974. Zbl0297.90082MR395227
15. 15. P. E. GILL et W. MURRAY, Safeguarded Steplength Algorithms for Optimization Using Descent Methods, N.P.L. Report NAC 37, 1974. 
16. 16. P. E. GILL, W. MURRAY, S. M. PICKEN et M. H. WRIGHT, The Design and Structure of a Fortran Program Library for Optimization, Report SOL 77-7, Stanford Univ., CA, 1977. Zbl0411.68029
17. 17. P. E. GILL, W. MURRAY et M. A. SAUNDERS, Methods for Computing and Modifying the LDV Factors of a Matrix, Math. Comp., 29, 1975, p. 1051. Zbl0339.65022MR388754
18. 18. A. GOMEZ et J. D. SEADER, Separation Sequences Synthesis by a Predictor Based Ordered Search, A.I.Ch.E. J., 22, 1976, p. 970. 
19. 19. D. GOLDFARB, Matrix Factorization in Optimization of Nonlinear Functions Subject to Linear Constraints, Math. Prog., 10, 1975, p.1. Zbl0374.90060MR406523
20. 20. D. GOLDFARB, Matrix Factorization in Optimization of Nonlinear Functions Subject to Linear Constraints - An Addendum, Math. Prog., 12, 1977, p. 279. Zbl0382.90082MR503798
21. 21. J. B. HENDRICKSON, A General Protocol for Synthesis Design, Topics in Current Chemistry, 62, 1976, p. 49. 
22. 22. E. HELLERMAN et D. RARICK, Reinversion with the Preassigned Pivot Procedure, Math. Prog., 1, 1971, p, 195. Zbl0246.65022MR293819
23. 23. E. HELLERMAN et D. RARICK, The Partitioned Preassigned Pivot Procedure (P4), in Sparse Matrices and their Applications, Plenum Press, 1972, p. 67. Zbl0246.65022MR331743
24. 24. HO THI DIEU, Optimisation continue d'un procédé chimique au moyen d'un calculateur analogique, Thèse M.S., Université de Laval, 1968. 
25. 25. L. S. LASDON, R. L. FOX et M. W. RATNER, Nonlinear Optimization Using the Generalized Reduced Gradient Method, R.A.I.R.O., 3, 1974, p. 73. Zbl0329.90060MR451713
26. 26. B. LINNHOFF, D. R. MASON et I. WARDLES, Understanding Heat Exchanger Networks, Comp. and Chem. Eng., 3, 1979, p. 295. 
27. 27. B. LINNHOFF et J. A. TURNER, Heat-Recovery Networks: New Insights Yield Big Savings, Chem. Eng., 11, 1981, p. 56. 
28. 28. M. A. MENZIES et A. I. JOHNSON, Synthesis of Optimal Energy Recovery Networks Using Discrete Methods, Can. J. Chem. Engineer., 50, 1972, p. 290. 
29. 29. W. MURRAY, Numerical Methods for Unconstrained Optimization, Academic Press, 1972. 
30. 30. B. A. MURTAGH, On the Simuitaneous Solution and Optimization of Large-Scale Engineering Systems, Comp. and Chem. Eng., 6, 1982, p.1. 
31. 31. B. A. MURTAGH et R. W. H. SARGENT, Computational Experience with Quadratically Convergent Minimization Methods, Comp. J., 13, 1970, p. 185. Zbl0202.16303MR266403
32. 32. B. A. MURTAGH et M. A. SAUNDERS, MINOS Use's Guide, Report SOL 77-9, Stanford Univ., CA, 1977. 
33. 33. B. A. MURTAGH et M. A. SAUNDERS, Nonlinear Programming for Large, Sparse Systems, Report SOL 76-15, Stanford Univ., CA, 1976. 
34. 34. B. A. MURTAGH et M. A. SAUNDERS, Large Scale Linearly Constrained Optimization, Math. Prog., 14, 1978, p. 41. Zbl0383.90074MR462607
35. 35. B. A. MURTAGH et M. A. SAUNDERS, The Implementation of a Lagrangian-Based Algorithm for Sparse Nonlinear Constraints, Report SOL 80-1, Stanford Univ., CA, 1980. 
36. 36. B. A. MURTAGH et M. A. SAUNDERS, MINOS/AUGMENTED User's Manual, Report SOL 80-14, Stanford Univ., CA, 1980. 
37. 37. P. V. PRECKEL, Modules for Use with MINOS/AUGMENTED, Report SOL 80-15, Stanford Univ., CA, 1980. 
38. 38. L. PIBOULEAU et S. DOMENECH, Une procédure arborescente pour la séparation de mélanges complexes dans l'industrie chimique, R.A.I.R.O., Rech. Op., 19, 1985, p. 35. Zbl0567.90063
39. 39. M. J. D. POWELL, A Note of Quasi-Newton Formulae for Sparse Second Derivative Matrices, Math. Prog., 20, 1981, p. 144. Zbl0453.90081MR607402
40. 40. R. N. S. RATHORE, K. A. VAN WORMER et G. J. POWELS, Synthesis Strategies for Multicomponent Separation Systems with Energy Integration, A.I.Ch.E.J., 20, 1974, p. 491. 
41. 41. F. R. RODRIGO et J. D. SEADER, Synthesis of Separation Sequences by Ordered Branch Search, A.I.Ch.E. J., 21, 1975, p. 885. 
42. 42. M. A. SAUNDERS, Large-Scale Linear Programming Using the Cholesky Factorization, Report STAN-CS-72-252, 1972. 
43. 43. M. A. SAUNDERS, MINOS System Manual, Report SOL77-31, Stanford Univ., CA, 1977. 
44. 44. M. A. SAUNDERS, MINOS Distribution Documentation, Report SOL 80-100, Stanford Univ., CA, 1980. 
45. 45. L. K. SCHUBERT, Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian, Math. Comp., 25, 1970, p, 27. Zbl0198.49402MR258276
46. 46. M. A. STADTHEER, G. D. GARY et R. C. ALKIRE, Optimization of an Electrolytic Cell with the Use of a GRG Algorithm, Comp. and Chem. Eng., 7, 1983, p. 27. 
47. 47. P. TOLLA, Amélioration de la stabilité numérique d'algorithmes de résolution de programmes linéaires à matrices de contraintes clairsemées, R.A.I.R.O., Rech.Op., 18, 1984, p.19. Zbl0576.90060MR737366
48. 48. J. A. TOMLIN, Modifying Triangular Factors of the Basis in the Simplex method, in Sparse Matrices and their Applications, Plenum Press, 1972, p. 77. Zbl0288.90048MR331743
49. 49. J. A. TOMLIN, On the Pricing and Backward Transformation in Linear Programming, Math. Prog., 6, 1974, p. 42. Zbl0278.90043MR337319
50. 50. J. VIGNES, Implementation des méthodes d'optimisation : Test d'arrêt optimal, contrôle et précision de la solution, R.A.I.R.O., Rech. Op., 18, 1984, p. 1. Zbl0601.65052MR737365
51. 51. P. WOLFE, Methods of Nonlinear Programming - the Reduced Gradient method, Recent Advances in Math. Progr., 67, 1963. Zbl0225.90042MR155683

1. X. Yuan, S. Zhang, L. Pibouleau, S. Domenech, Une méthode d'optimisation non linéaire en variables mixtes pour la conception de procédés