A complementarity-based partitioning and disjunctive cut algorithm for mathematical programming problems with equilibrium constraints

Journal of Global Optimization

Volumn 36, Issue 1, 2006, Pages 89-114

  Júdice, Joaquim J ^a   Sherali, Hanif D ^b   Ribeiro, Isabel M ^c   Faustino, Ana M ^c  

^a UNIVERSITY OF COIMBRA   (Portugal)

^b State University   (United States)

^c UNIVERSITY OF PORTO   (Portugal)

Author keywords

Active set algorithm; Branch and bound method; Complementarity; Disjunctive cuts; Global optimization

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; GLOBAL OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

ACTIVE-SET ALGORITHM; BRANCH-AND-BOUND METHOD; COMPLEMENTARITY; DISJUNCTIVE CUTS;

MATHEMATICAL PROGRAMMING;

EID: 33747162443     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-006-9001-8     Document Type: Article

References (24)

1. Balas, E. (1979), Disjunctive programming, Annals of Discrete Mathematics 5, 3-51.
2. Bard, J. and Moore, J. (1990), A branch-and-bound algorithm for the bilevel linear program, SIAM Journal on Scientific and Statistical Computing 11, 281-292.
3. Breiman, L. (1993). Hinging hyperplanes for regression, classification and function approximation, IEEE Transactions on Information Theory 39, 999-1013.
4. Calamai, P. and Vicente, L. (1993), Generating linear and linear-quadratic bilevel programming problems, SIAM Journal on Scientific Computing 14, 770-782.
5. Calamai, P. and Vicente, L. (1994). Generating quadratic bilevel programming test problems, ACM Transactions on Mathematical Software 20, 103-119.
6. Facchinei, F., Jiang, H. and Qi, L. (1999). A smoothing method for mathematical programs with equilibrium constraints, Mathematical Programming 85, 107-134.
7. Fletcher, R., Leyffer, S. and Toint, P. (2002), On the global convergence of a filter-sqp algorithm, SIAM Journal on Optimization 13(1), 44-59.
8. Fukushima, M., Luo, Z. and Pang J. (1998). A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints, Computational Optimization and Applications 10, 5-34.
9. Hansen, P., Jaumard, B. and Savard, G. (1992), New branch-and-bound rules for linear bilevel programming, SIAM Journal on Scientific Computing 13(5). 1194-1217.
10. Jiang, H. and Ralph, D. (2000), Smooth sqp methods for mathematical programs with nonlinear complementarity constraints. SIAM Journal on Optimization 10(3). 779-808.
11. Júdice, J. and Faustino, A. (1991), A computational analysis of lcp methods for bilinear and concave quadratic programming, Computers and Operations Research 18, 645-654.
12. Júdice, J. and Faustino, A. (1992), A sequential lcp algorithm for bilevel linear programming, Annals of Operations Research 34, 89-106.
13. Judice, J., Faustino, A. and Ribeiro, I. (2002), On the solution of np-hard linear complementarity problems. TOP-Sociedad de Estatistica e Investigation Operativa 10(1). 125-145.
14. Júdice. J., Sherali, H., Ribeiro, I. and Faustino, A. (2005). A complementarity active-set algorithm for mathematical programming problems with equilibrium constraints, Working Paper.
15. Júdice, J. and Vicente, L. (1994), On the solution and complexity of a generalized linear complementarity problem. Journal of Global Optimization 4, 415-424.
16. Luo, Z., Pang, J. and Ralph, D. (1997). Mathematical Programs with Equilibrium Constraints, Cambridge University Press. New York.
17. Murtagh, B. and Saunders, A. (1983), MINOS 5.0 User's Guide, Technical Report SOL 83-20, Department of Operations Research, Stanford University.
18. Nocedal, J. and Wright, S. (1999), Numerical Optimization, Springer-Verlag, New York, N.Y.
19. Pucar, P. and Sjoberg, J. (1998). On the hinge finding algorithm for hinging hyperplanes, IEEE Transactions on Information Theory 44, 1310-1318.
20. Queiroz, M., Humes Jr, C. and Júdice, J. (2004), On finding global optima for the hinge fitting problem. Computers and Operations Research 31, 101-122.
21. Ribeiro, I. (2005), Global Optimization and Applications to Structural Engineering (in Portuguese). PhD thesis. University of Porto. Porto.
22. Scholtes, S. (1999), Active set methods for inverse linear complementarity problems, Judge Institute of Management Research Paper Series No. 28/1999.
23. Sherali, H. and Shetty, C. (1980). Optimization with disjunctive constraints, In: Beckman, M. and Künzi, H. (eds.), Lecture Notes in Economics and Mathematical Systems, Vol. 181, Springer-Verlag, New York, N.Y.
24. White, D. and Annandalingam, G. (1993), A penalty function approach for solving bilevel linear programs, Journal of Global Optimization 3, 397-419.