A method for obtaining continuous solutions to multiparametric linear programs

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue , 2005, Pages 253-258

  Spjøtvold, Jørgen ^a   Tøndel, Petter ^a   Johansen, Tor A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Constrained optimal control; Explicit model predictive control; Linear programming; Multiparametric programming; Quadratic programming

Indexed keywords

CONSTRAINED OPTIMIZATION; MODEL PREDICTIVE CONTROL; QUADRATIC PROGRAMMING;

CONSTRAINED OPTIMAL CONTROL; EXPLICIT MODEL PREDICTIVE CONTROL; GEOMETRIC ALGORITHM; LINEAR PROGRAMS; MULTI-PARAMETRIC PROGRAMMING; NON-UNIQUE SOLUTIONS; PIECEWISE AFFINES; SOLUTION SPACE;

LINEAR PROGRAMMING;

EID: 79960742655     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00903     Document Type: Conference Paper

References (25)

1. Acevedo, J. and E. N. Pistikopoulos (1997). A multiparametric programming approach for linear process engineering problems under uncertainty. Ind. Eng. Chem. Res. 36, 717-728.
2. Bank, B., J. Guddat, D. Klatte, B. Kummer and K. Tammer (1983). Non-linear Parametric Optimization. Birkhäuser. Berlin.
3. Bemporad, A., F. Borrelli and M. Morari (2002a). Model predictive control based on linear programming - the explicit solution. IEEE Trans. on Automatic Control 47(12), 1974-1985.
4. Bemporad, A., M. Morari, V. Dua and E. N. Pistikopoulos (2002b). The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3-20.
5. Berge, C. (1963). Topological Spaces. Oliver and Boyd Ltd. London.
6. Best, M. J. and B. Ding (1972). On the continuity of the minimum in parametric quadratic programs. Journal of Optimization Theory and Applications 86(1), 245-250.
7. Bohm, V. (1975). On the continuity of the optimal policy set for linear programs. SIAM Journal on Applied Mathematics 28, 303-306.
8. Borrelli, F., A. Bemporad and M. Morari (2003). A geometric algorithm for multi-parametric linear programming. Journal of Optimization Theory and Applications 118(3), 515-540.
9. Dantzig, G. B., J. Folkman and N. Z. Shapiro (1967). On the continuity of the minimum set of a continuous function. Journal of Mathematical Analysis and Applications 17(3), 519-548.
10. Dinkelbach, W. (1969). Sensitivitiätsanalysen und parametrische Programmierung. Springer. Berlin.
11. Fiacco, A. V. (1983). Introduction to sensitivity and stability analysis in nonlinear programming. Academic Press Inc.. Orlando, FL.
12. Gal, T. (1995). Postoptimal Analyses, Parametric Programming, and Related Topics. second ed.. de Gruyter. Berlin.
13. Gal, T. and J. Nedoma (1972). Multiparametric linear programming. Managment Science 18, 406-442.
14. Güler, O. and Y. Ye (1993). Convergence behavior of interior-point algorithms. Mathematical Programming 60, 215-228.
15. Jones, C. N., E. C. Kerrigan and J. M. Maciejowski (2004). Equality set projection: A new algorithm for the projection of ploytopes in halfspace representation. Technical Report CUED/F-INFENG/TR.463. Deparment of Engineering, University of Cambridge. Cambridge, UK.
16. Mangasarian, O. L. (1979). Uniqueness of solution in linear programming. Linear Algebra and its Applications 25, 151-162.
17. Michaels, E. (1956). Continuous selections. Annals of Mathematics 63, 361-382.
18. Schechter, M. (1987). Polyhedral functions and multi-parametric linear programming. Journal of Optimization Theory and Applications 53, 269-280.
19. Spjøtvold, J., P. Tøndel and T. A. Johansen (2005). Unique polyhedral representations of continuous selections for convex multiparametric quadratic programs. In: Proc. American Contr. Conf.. Portland.
20. Tøndel, P., T. A. Johansen and A. Bemporad (2003a). An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica 39(3), 489-497.
21. Tøndel, P., T. A. Johansen and A. Bemporad (2003b). Further results on multi-parametric quadratic programming. In: Proc. 42nd IEEE Conf. on Decision and Control. Hawaii. pp. 3173-3178.
22. van der Panne, C. (1975). A node method for multiparametric linear programming. Management Science 21, 1014-1020.
23. Yu, P. L. and M. Zeleny (1976). Linear multiparametric programming by multicirteria simplex method. Management Science 23, 159-170.
24. Zhang, X. S. and D. G. Liu (1990). A note on the continuity of solutions of parametric linear programming. Mathematical Programming 47, 143-153.
25. Zhao, J. (1997). The lower continuity of optimal solution sets. Journal of Mathematical Analysis and Applications 207, 240-250.