Global solution of optimization problems with parameter-embedded linear dynamic systems

Journal of Optimization Theory and Applications

Volumn 121, Issue 3, 2004, Pages 613-646

  Singer, A B ^a   Barton, P I ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

convex underestimators; Deterministic global optimization; interval analysis; linear systems theory

Indexed keywords

BRANCH AND BOUND METHOD; EMBEDDED SYSTEMS; GLOBAL OPTIMIZATION; RELAXATION PROCESSES;

CONVEX UNDERESTIMATORS; DETERMINISTIC GLOBAL OPTIMIZATION; GLOBAL MINIMUM; GLOBAL SOLUTIONS; INTERVAL ANALYSIS; LINEAR DYNAMIC SYSTEM; LINEAR-SYSTEM THEORY; NONCONVEX OPTIMIZATION PROBLEM; OPTIMIZATION PROBLEMS; PROBLEM FORMULATION;

LINEAR CONTROL SYSTEMS;

EID: 4444340330     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000037606.79050.a7     Document Type: Article

References (34)

1. TROUTMAN, J., Variational Calculas and Optimal Control: Optimization with Elementary Convexity, 2nd Edition, Springer Verlag, New York, NY, 1996.
2. PONTRYAGIN, L., The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, NY, 1962.
3. TSANG, T., HIMMELBLAU, D., and EDGAR, T., Optimal Control via Collocation and Nonlinear Programing, International Journal of Control, Vol. 21, pp. 763-768, 1975.
4. NEUMAN, C., and SEN, A., A Suboptimal Control Algorithm for Constrained Problems Using Cubic Splines, Automatica, Vol. 9, pp. 601-613, 1973.
5. BRUSCH, R., and SCHAPPELLE, R., Solution of Highly-Constrained Optimal Control Problems Using Nonlinear Programming, AIAA Journal, Vol. 11, pp. 135-136, 1973.
6. TEO, K., GOH, G., and WONG, K., A Unified Computational Approach to Optimal Control Problems, Pitman Monographs and Surveys in Pure and Applied Mathematics, John Wiley and Sons, New York, NY, 1991.
7. ESPOSITO, W. R., and FLOUDAS, C. A., Global Optimization for the Parameter Estimation of Differential-Algebraic Systems, Industrial and Engineering Chemical Research, Vol. 39, pp. 1291-1310, 2000.
8. ESPOSITO, W. R., and FLOUDAS, C. A., Deterministic Global Optimization in Nonlinear Optimal Control Problems, Journal of Global Optimization, Vol. 17, pp. 97-126, 2000.
9. PAPAMICHAIL, I., and ADJIMAN, C. S., A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations, Journal of Global Optimization, Vol. 24, pp. 1-33, 2002.
10. CODDINGTON, E. A., and LEVINSON, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, NY, 1955.
11. ASCHER, U. M., and PETZOLD, L. R., Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, Pennsylvania, 1998.
12. ZADEH, L. A., and DESOER, C. A., Linear System Theory: The State Space Approach, McGraw-Hill, New York, NY, 1963.
13. MATTUCK, A., Introduction to Analysis, Prentice Hall, Englewood Cliffs, New Jersey, 1999.
14. RUDIN, W., Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill, New York, NY, 1976.
15. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
16. HORST, R., and TUY, H., Global Optimization, Springer Verlag, Berlin, Germany, 1993.
17. MOORE, R. E., Methods and Applications of Interval Analysis, SIAM, Philadelphia, Pennsylvania, 1979.
18. MCCORMICK, G. P., Computability of Global Solutions to Factorable Nonconvex Programs: Part I: Convex Underestimating Problems, Mathematical Programming, Vol. 10, pp. 147-175, 1976.
19. MARANAS, C., and FLOUDAS, C., Global Minimum Potential Energy Conformations of Small Molecules, Journal of Global Optimization, Vol. 4, pp. 135-170, 1994.
20. ADAMS, M., and GUILLEMIN, V., Measure Theory and Probability, Birkhäuser, Boston, Massachusetts, 1996.
21. RYOO, H., and SAHINDIS, N., Global Optimization of Nonconvex NLPs and MINLPs with Application in Process Design, Computers and Chemical Engineering, Vol. 19, pp. 551-566, 1995.
22. RYOO, R., and SAHINDIS, N., A Branch-and-Reduce Approach to Global Optimization, Journal of Global Optimization, Vol. 2, pp. 107-139, 1996.
23. GILL, P. E., MURRAY, W., SAUNDERS, M. A., and WRIGHT, M. H., User's Guide for NPSOL 5.0: A Fortran Package for Nonlinear Programming, Technical Report, Stanford University, 1998.
24. FEEHERY, W., TOLSMA, J., and BARTON, P., Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Systems, Applied Numerical Mathematics, Vol. 25, pp. 41-54, 1997.
25. TOLSMA, J. E., and BARTON, P. I., DAEPACK: A Symbolic and Numeric Library for Open Modeling, http://yoric.mit.edu/daepack/daepack.html.
26. TOLSMA, J. and BARTON, P. I., DAEPACK: An Open Modeling Environment for Legacy Models, Industrial and Engineering Chemistry Research, Vol. 39, pp. 1826-1839, 2000.
27. BAZARAA, M. S., SHERALI, H. D., and SHETTY, C., Nonlinear Programming: Theory and Algorithms, 2nd Edition, John Wiley and Sons, New York, NY, 1993.
28. UTKIN, V. I., Sliding Modes in Control and Optimization, Springer Verlag, Berlin, Germany, 1992.
29. CARVER, M. B., Efficient Integration over Discontinuities in Ordinary Differential Equation Simulations, Mathematics and Computers in Simulation, Vol. 20, pp. 190-196, 1978.
30. ADJIMAN, C., DALLWIG, S., FLOUDAS, C., and NEUMAIER, A., A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs, I: Theoretical Advances, Computers and Chemical Engineering, Vol. 22, pp. 1137-1158, 1998.
31. MCCORMICK, G. P., Nonlinear Programming: Theory, Algorithms, and Applications, John Wiley and Sons, New York, NY, 1983.
32. ADJIMAN, C., DALLWIG, S., and FLOUDAS, C., A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs, II: Implementation and Computational Results, Computers and Chemical Engineering, Vol. 22, pp. 1159-1179, 1998.
33. PANTELIDES, C. C., Speedup: Recent Advances in Process Simulation, Computers and Chemical Engineering, Vol. 12, pp. 745-755, 1988.
34. PARK, T., and BARTON, P. I., State Event Location in Differential Algebraic Models, ACM Transactions on Modelling and Computer Simulation, Vol. 6, pp. 137-165, 1996.