Parametric global optimisation for bilevel programming

Journal of Global Optimization

Volumn 38, Issue 4, 2007, Pages 609-623

  Faísca, Nuno P ^a   Dua, Vivek ^b   Rustem, Berç ^a   Saraiva, Pedro M ^c   Pistikopoulos, Efstratios N ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Bilevel programming; Mixed integer; Parametric programming; Quadratic; Uncertainty

Indexed keywords

ALGORITHMS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; PARAMETER ESTIMATION; PROBLEM SOLVING; UNCERTAINTY ANALYSIS;

BILEVEL PROGRAMMING; INTEGER LINEAR PROBLEMS; MIXED-INTEGERS; PARAMETRIC PROGRAMMING;

GLOBAL OPTIMIZATION;

EID: 34250821129     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-006-9100-6     Document Type: Conference Paper

References (38)

1. Acevedo, J., Pistikopoulos, E.N.: A multiparametric programming approach for linear process engineering problems under uncertainty. Ind. Eng. Chem. Res. 36, 717-728 (1997)
2. Aiyoshi, E., Shimizu, K.: Hierarchical decentralized systems and its new solution by a barrier method. IEEE Trans. Syst. Man Cybern. 11(6), 444-449 (1981)
3. Başar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. Academic Press, London (1982) Bard, J.F., Falk, J.: An explicit solution to the multi-level programming problem. Comput. Oper. Res. 9, 77-100 (1982)
4. Cao, D., Chen, M.: Capacitated plant selection in a decentralized manufacturing environment: a bilevel optimization approach. Eur. J. Oper. Res. 169(1), 97-110 (2006)
5. Clark, P.A.: Bilevel programming for steady-state chemical process design -II. performance study for nondegenerate problems. Comput. Chem. Eng. 14(1), 99-109 (1990)
6. Clark, P.A., Westerberg, A.W.: Bilevel programming for steady-state chemical process design - I. fundamentals and algorithms. Comput. Chem. Eng. 14(1), 87-97 (1990)
7. Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optim. 52(3), 33-359 (2003)
8. Dempe, S., Kalashnikov, V., Ríos-Mercado, R.Z.: Discrete bilevel programming: Application to a natural gas cash-out problem. Eur. J. Oper. Res. 166, 469-488 (2005)
9. Deng, X.: Complexity issues in bilevel linear programming. In: Pardalos, P.M., Varbrand, P., Migdalas, A. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 149-164. Kluwer Academic Publishers. Dordrecht (1998)
10. Dua, V.: Parametric programming techniques for process engineering problems under uncertainty. PhD thesis. Department of Chemical Engineering and Chemical Technology Imperial College of Science, Technology and Medicine London, UK (2000)
11. Dua, V., Pistikopoulos, E.N.: An algorithm for the solution of multiparametric mixed integer linear programming problems. Ann. Oper. Res. 99, 123-139 (2000)
12. Dua, V., Bozinis, A., Pistikopoulos, E.N.: A multiparametric programming approach for mixed-integer quadratic engineering problems. Comput. Chem. Eng. 26, 715-733 (2002)
13. Evans, G.W.: An overview of thecniques for solving multiobjective mathematical programs. Manage. Sci. 30(11), 1268-1282 (1984)
14. Fiacco, A.V.: Sensitivity analysis for nonlinear programming using penalty methods. Math. Program. 10, 287-311 (1976)
15. Fiacco, A.V.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York (1983)
16. Floudas, C.A.: Deterministic Global Optimization. Kluwer Academic Publishers, Dordrecht, (2000)
17. Floudas, C.A., Pardalos, P.M., Adjiman, C.S., Esposito, W.R., Gümüs, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., Schweiger, C.A.: Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publisher, Dordrecht (1999)
18. Fortuny-Amat, J., McCarl, B.: A representation and economic interpretation of a two-level programming problem. J Oper. Res. Soc. 32(9), 783-792 (1981)
19. Gal, T.: Postoptimal Analyses. Parametric Programming, and Related Topics, de Gruyter, New York, (1995)
20. Hansen, P., Jaumard, B., Savard, G.: New brach-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13, 1194-1217 (1992)
21. Lai, Y.: Hierarchical optimization: a satisfactory solution. Fuzzy Sets Syst. 77, 321-335 (1996)
22. LeBlanc, L.J., Boyce, D.E.: A bilevel programming algorithm for exact solution of network design problemwith user-optimal flows. Trans. Res. - Part B Meth. 20, 259-265 (1985)
23. Liu, B.: Stakelberg-nash equilibrium for multilevel programming with multiple followers using genetic algorithms. Comput. Math. Appl. 36(7), 79-89 (1998)
24. Muu, L.D.. Quy, N.V.: A global optimization method for solving convex quadratic bilevel pogramming problems. J. Global Optim. 26, 199-219 (2003)
25. Ruan, G.Z., Wang, S.Y., Yamakamoto, Y., Zhu, S.S.: Optimality conditions and geometric properties of linear multilevel programming problem with dominated objective functions. J Optim. Theory Appl. 123(2), 409-429 (2004)
26. Ryu, J., Dua, V., Pistikopoulos, E.N.: A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput. Chem. Eng. 28, 1121-1129 (2004)
27. Sakizlis, V., Perkins, J.D., Pistikopoulos, E.N.: Parametric controllers in simultaneous process and control design optimization. Ind. Eng. Chem. Res. 42, 4545-4563 (2003)
28. Sakizlis, V., Perkins, J.D., Pistikopoulos, E.N.: Recent advances in optimization-based simulataneous process and control design. Comput. Chem. Eng. 28(10), 2069-2086 (2004a)
29. Sakizlis, V., Kakalis, M.P., Dua, V., Perkins, J.D., Pistikopoulos, E.N.: Design of robust controllers via parametric programming. Automatica 40, 189-201 (2004b)
30. Shih, H., Lai, Y., Lee, E.S.: Fuzzy approach for multi-level programming problems. Comput. Oper. Res. 23(1), 73-91 (1996)
31. Shimizu, K., Ishizuka, Y., Bard, J.F.: Nondifferentiable and Two-Level Mathematical Programming. Kluwer Academic Press, Boston (1997)
32. Stephanopoulos, G., Ng, C.: Perspectives on the synthesis of plant-wide control structures. J. Process Control 10, 97-111 (2000)
33. Tabucanon, M.T.: Multiple Criteria Decision Making in Industry. Elsevier, Amsterdam (1988)
34. Vicente, L.N., Calamai, PH.: Bilevel and multilevel programming: A bibliography review. J. Global Optim. 5(3), 291-306 (1994a)
35. Vicente, L.N., Savard, G.. Júdice, J.: Descent approaches for quadratic bilevel programming. J. Optim. Theory Appl. 81, 379-399 (1994b)
36. Vicente, L.: Bilevel programming. Master's thesis. Department of Mathematics, University of Coimbra, Coimbra (1992)
37. Visweswaran, V., Floudas, M.G., lerapetritou, CA., Pistikopoulos, E.N.: A decomposition-based global optimization approach for solving bilevel linear and quadratic programs. In: Floudas, C. A., Pardalos, P.M. (eds.) State of the Art in Global Optimization, pp. 139-162. Kluwer Academic Publishers, Dordrecht (1996)
38. Wen, U.P. Yang, Y.H.: Algorithms for solving the mixed integer two-level linear programming problem. Comput. Oper. Res. 17(2), 133-142 (1990)