Global optimization in generalized geometric programming

Computers and Chemical Engineering

Volumn 21, Issue 4, 1997, Pages 351-369

  Maranas, Costas D ^a   Floudas, Christodoulos A ^a  

^a Princeton University   (United States)

Author keywords

Generalized geometric programming; Global optimization; Robust stability analysis; Signomials

Indexed keywords

ALGORITHMS; CHEMICAL ENGINEERING; CHEMICAL EQUIPMENT; CHEMICAL REACTORS; COMPUTER PROGRAMMING; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS);

COMPUTER AIDED DESIGN;

EID: 0030871124     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(96)00282-7     Document Type: Article

References (51)

1. Abate M., Barmish B.R., Murillo-Sanchez C. and Tempo R., Application of Some New Tools to Robust Stability Analysis of Spark Ignition Engines: A Case Study, IEEE Trans. Contr. Syst. Tech., 2, 1 (1994) 22
2. Abrams R.A. and Wu C.T., Projection and restriction methods in geometric and related problems, JOTA, 26, (1978) 59
3. Ackermann J., Kaesbauer D. and Muench R., Robust Gamma-Stability Analysis in a Plant Parameter Space, Automatica, 27, (1991) 75
4. Avriel M. and Wilde D.J., Optimal Condenser Design by Geometric Programming, I&EC Proc. Des. Dev., 6, (1967) 256
5. Avriel M. and Gurovich V., Optimal Condenser Design by Geometric Programming, I&EC Proc. Des. Dev., 6, (1967) 256
6. Avriel M. and Williams A.C., Complementary geometric programming, SIAM J. Appl. Math., 19, (1970) 125
7. Avriel M., Dembo R. and Passy U., Solution of generalized geometric programs, SIAM Intern. J. Numer. Methods Engnr., 26, (1975) 291
8. Avriel M., Dembo R. and Passy U., Solution of Generalized Geometric Programs, International Journal for Numerical Methods in Engineering, 9, (1975) 149
9. Avriel M. and Williams A.C., An Extension of Geometric Programming with Applications in Engineering Optimization, Journal of Engineering Mathematics., 5, 3 (1971) 187
10. Barmish B. R., New Tools for Robustness of Linear Systems. Macmillan Publishing Company, New York (1994).
11. Beck P.A. and Ecker J.G., A modified concave simplex algorithm for geometric programming, JOTA, 15, (1975) 189
12. Blau G.E. and Wilde D.J., Generalized Polynomial Programming, Can. J. Chem. Eng., 47, (1969) 317
13. Blau G.E. and Wilde D.J., A lagrangian algorithm for equality constrained generalized polynomial optimization, AIChE, 17, (1971) 235
14. Bradley, J., An algorithm for the numerical solution of prototype geometric programs. Institute of Industrial Research and Standards, Dublin, Ireland (1973).
15. Daston R.R.E. and Safonov M.G., Exact Calculation of the Multi-Loop Stability Margin, IEEE Trans. Automat. Contr., 33, (1988) 68
16. Duffin R.J. and Peterson E.L., Duality theory for geometric programming, SIAM J. Appl. Math., 14, (1966) 1307
17. Duffin R.J. and Peterson E.L., Reversed geometric programming treated by harmonic means, Indiana Univ. Math. J., 22, (1972) 531
18. Dembo R.S., Optimal design of a membrane separation process using signomial programming, Math. Prog., 15, (1978) 12
19. Dembo R.S., Current state of the art of algorithms and computer software for geometric programming, JOTA, 26, (1978) 149
20. Duffin R.J., Linearizing geometric problems, SIAM Review, 12, (1970) 211
21. Dembo R.S., A Set of Geometric Programming Test Problems and their Solutions, Math. Prog., 10, (1976) 192
22. Ecker J.G. and Wiebking R.D., Optimal design of a dry-type natural-draft cooling tower by geometric programming, JOTA, 26, (1978) 305
23. Falk, J. E., Global Solutions of Signomial Programs, Report, The George Washington University, Program in Logistics, (1973).
24. Floudas C.A. and Visweswaran V., A global optimization algorithm (GOP) for certain classes of nonconvex NLP's: I. Theory, Comput. chem. Engng., 12, 14 (1990) 1397
25. Floudas C.A. and Visweswaran V., A primal-relaxed dual global optimization approach, Journal of Optimization Theory and Applications, 78, 2 (1993) 187
26. Hansen P., Jaumard B. and Lu S.H., Some Further Results on Monotonicity in Globally Optimal Design, Journal of Mechanisms, Transmissions, and Automation in Design, 111, (1989) 345
27. Haarhoff P.C. and Buys J.D., A new method for the optimization of a nonlinear function subject to nonlinear constraints, Comp. J., 13, (1970) 178
28. Hellinckx L.J. and Rijckaert M.J., Optimal Capacities of Production Facilities: An Application of geometric programming, Can. J. Chem. Eng., 50, (1972) 148
29. Hellinckx L.J. and Rijckaert M.J., Minimization of capital investment for batch processes, I&EC Proc. Des. Dev., 10, (1971) 422
30. Horst R. and H. Tuy, Global Optimization, Deterministic Approaches. Springer-Verlag, Berlin (1990).
31. Jefferson T.R. and Scott C.H., Generalized geometric program ming applied to problems of optimal control: I. Theory, JOTA, 26, (1978) 117
32. Kochenberger A., Woolsey R.E.D. and McCarl B.A., On the solution of geometric programming via separable programming, Oper. Res. Quart., 24, (1973) 285
33. Kuester, J. L. and Mize, J. H., Optimization Techniques with Fortran. McGraw-Hill Book Company, New York, NY (1973).
34. Liu W.B. and Floudas C.A., A remark on the GOP algorithm for global optimization. Journal of Global Optimization, 3, (1994) 519
35. Manousiouthakis V. and Sourlas D., A Global Optimization Approach to Rationally Constrained Rational Programming, Chem. Eng. Comm., 115, (1992) 127
36. Maranas C.D. and Floudas C.A., A Global Optimization Approach for Lennard-Jones Microclusters, J. Chem. Phys., 97, 10 (1992) 7667
37. Maranas C.D. and Floudas C.A., Global Optimization for Molecular Conformation Problems, Annals of Operations Research, 42, (1993) 85
38. Maranas C.D. and Floudas C.A., Global Minimum Potential Energy Conformations of Small Molecules, Journal of Global Optimization, 4, (1994) 135
39. Maranas C.D. and Floudas C.A., A Deterministic Global Optimization Approach for Molecular Structure Determination, J. Chem. Phys., 100, 2 (1994) 1247
40. Murtagh B. A. and M. A. Saunders, MINOS 5.3 User's Guide. Systems Optimization Laboratory, Department of Operations Research, Stanford University (1987).
41. Passy U. and Wilde D.J., Generalized polynomial optimizations, SIAM J. Appl. Math., 15, (1967) 1344
42. Passy U. and Wilde D.J., A geometric programming algorithm for solving chemical equilibrium problems, SIAM Review, 11, (1967) 89
43. Psarris P. and C. A. Floudas, Robust Stability Analysis of Linear and Nonlinear Systems with Real Parameter Uncertainty. submitted, 1994.
44. Ratner M., Lasdon L.S. and Jain A., Solving geometric problems using GRG: Results and comparisons, JOTA, 26, (1978) 253
45. Rijckaert M.J. and Martens X.M., Bibliographical note on geometric programming, JOTA, 2, (1978) 325
46. Rijckaert and Martens X.M., Comparison of generalized geometric programming algorithms, JOTA, 26, (1978) 205
47. Ryoo H.S. and Sahinidis N.V., Global Optimization of Non-convex NLPs and MINLPs with Applications in Process Design. Computers chem. Engng, 19, 5 (1995) 551
48. Sideris A. and R. S. Sànchez Peña, Fast Computation of the Multivariable Stability Margin for Real Interrelated Uncertain Parameters. In Proc. ACC, Atlanta, Ga (1988).
49. Salomone H.E. and Iribarren O.A., Posynomial modeling of batch plants: A procedure to include process decision variables. Computers chem. Engng, 16, (1992) 173
50. Vicìno A., Tesi A. and Milanese M., Computation of Non-conservative Stability Perturbation Bounds for Systems with Nonlinearly Correlated Uncertainties, IEEE Trans. Autom. Contr., 35, (1990) 835
51. Visweswaran V. and Floudas C.A., New properties and computational improvement of the GOP algorithm for problems with quadratic objective functions and constraints, Journal of Global Optimization, 3, (1993) 439