An extended Kth-best approach for linear bilevel programming

Applied Mathematics and Computation

Volumn 164, Issue 3, 2005, Pages 843-855

  Shi, Chenggen ^a   Lu, Jie ^a   Zhang, Guangquan ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Kth best approach; Linear bilevel programming; Optimization; Von Stackelberg game

Indexed keywords

ALGORITHMS; FUNCTIONS; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

KTH-BEST APPROACH; KUHN-TUCKER APPROACH; LINEAR BILEVEL PROGRAMMING; VON STACKELBERG GAME;

LINEAR PROGRAMMING;

EID: 16344368494     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.06.047     Document Type: Article

References (15)

1. H. Von Stackelberg The Theory of the Market Economy 1952 Oxford University Press York, Oxford
2. J. Bard Practical Bilevel Optimization: Algorithms and Applications 1998 Kluwer Academic Publishers USA
3. W. Candler, and R. Townsley A linear two-level programming problem Computers and Operations Research 9 1982 59 76
4. W. Bialas, and M. Karwan Two-level linear programming Management Science 30 1984 1004 1020
5. J. Bard, and J. Falk An explicit solution to the multi-level programming problem Computers and Operations Research 9 1982 77 100
6. W. Bialas, M. Karwan, Multilevel linear programming. Technical Report 78-1, State University of New York at Buffalo, Operations Research Program, 1978
7. P. Hansen, B. Jaumard, and G. Savard New branch-and-bound rules for linear bilevel programming SIAM Journal on Scientific and Statistical Computing 13 1992 1194 1217
8. W. Bialas, M. Karwan, J. Shaw, A parametric complementary pivot approach for two-level linear programming. Technical Report 80-2, State University of New York at Buffalo, Operations Research Program, 1980
9. E. Aiyoshi, and K. Shimizu Hierarchical decentralized systems and its new solution by a barrier method IEEE Transactions on Systems, Man, and Cybernetics 11 1981 444 449
10. D. White, and G. Anandalingam A penalty function approach for solving bi-level linear programs Journal of Global Optimization 3 1993 397 419
11. J. Bard An investigation of the linear three level programming problem IEEE Transactions on Systems, Man, and Cybernetics 14 1984 711 717
12. G. Savard, Contributions á la programmation mathématique á deux niveaux, Ph.D. thesis, Université de Montréal, École Polytechnique, 1989
13. C. Shi, G. Zhang, J. Lu, On the definition of linear bilevel programming solution, Applied Mathematics and Computation, in press
14. C. Shi, J. Lu, G. Zhang, An extended Kuhn-Tucker approach for linear bilevel programming, Applied Mathematics and Computation, in press
15. University of Cambridge. Available from: < http://thesaurus.maths.org/ dictionary/map/word/10037 >, 2001