Summary of QP-QP bilevel problems
Description of the Quadratic-Quadratic bilevel test problems: data and references
| Label | Source | n | m | F* | f* | x* | y* |
|---|---|---|---|---|---|---|---|
| b_1998_04 | (Bard, 1998) | 1 | 1 | 81.330 | -0.336 | 10.020 | 0.820 |
| b_1998_05 | (Bard, 1998) | 1 | 1 | 1.000 | 0.000 | 1.000 | 0.000 |
| lmp_1987_01 | (Lucchetti et al., 1987) | 1 | 1 | 0.000 | 0.000 | 1.000 | 0.000 |
| y_1996_02 | (Yezza, 1996) | 1 | 1 | 1.500 | -2.500 | 0.250 | 0.000 |
| d_1992_01 | (Dempe, 1992) | 1 | 1 | 31.250 | 4.000 | 1.000 | 1.000 |
| d_2000_01 | (Dempe, 2000) | 1 | 1 | 0.000 | -0.250 | 0.500 | -0.500 |
| cw_1990_02 | (Clark & Westerberg, 1990) | 1 | 1 | 5.000 | 4.000 | 1.000 | 3.000 |
| tmh_2007_01 | (Tuy et al., 2007) | 1 | 1 | 22.500 | -4.500 | 1.500 | 4.500 |
| b_1988_01 | (Bard, 1988) | 1 | 1 | 17.000 | 1.000 | 1.000 | 0.000 |
| sa_1981_01 | (Shimizu & Aiyoshi, 1981) | 1 | 1 | 100.000 | 0.000 | 10.000 | 10.000 |
| sc_1998_01 | (Sahin & Ciric, 1998) | 1 | 1 | 9.000 | 0.000 | 3.000 | 5.000 |
| b_1998_02 | (Bard, 1998) | 2 | 1 | 0.000 | -0.900 | (0.800, 0.200) | 1.000 |
| b_1998_03 | (Bard, 1998) | 2 | 1 | 0.000 | -0.320 | (1.000, 0.400) | 0.800 |
| b_1998_07 | (Bard, 1998) | 1 | 2 | 1.410 | 7.620 | 1.890 | (0.890, 0.000) |
| d_1978_01 | (De Silva, 1978) | 2 | 2 | -1.000 | 0.000 | (0.500, 0.500) | (0.500, 0.500) |
| fl_1995_01 | (Falk & Liu, 1995) | 2 | 2 | -2.250 | 0.000 | (0.750, 0.750) | (0.750, 0.750) |
| sa_1981_02 | (Shimizu & Aiyoshi, 1981) | 2 | 2 | 225.000 | 100.000 | (20.000, 5.000) | (10.000, 5.000) |
| b_1984_02 | (Bard, 1984) | 2 | 2 | -12.680 | -1.016 | (0.000, 2.000) | (1.875, 0.906) |
| dd_2012_02 | (Dempe & Dutta, 2012) | 2 | 2 | -1.000 | 4.000 | (0.707, 0.707) | (0.000, 1.000) |
| as_1981_02 | (Aiyoshi & Shimizu, 1981) | 4 | 4 | -6600.0 | 54.000 | (7.0, 3.0, 12.0, 18.0) | (0.0, 10.0, 30.0, 0.0) |
References
- E. Aiyoshi and K. Shimizu, Hierarchical decentralized systems and its new solution by a barrier method, IEEE Transactions on Systems, Man and Cybernetics, (1981), pp. 444-449
- J. F. Bard, Optimality conditions for the bilevel programming problem, Naval research logistics quarterly, 31 (1984), pp. 13–26
- J. F. Bard, Convex two-level optimization, Mathematical Programming, 40 (1988), pp. 15–27
- J. F. Bard, Practical Bilevel Optimization, vol. 30 of Nonconvex Optimization and Its Applications, Springer US, 1998
- P. A. Clark and A. W. Westerberg, Bilevel programming for steady-state chemical process design-I. fundamentals and algorithms, Computers & Chemical Engineering, 14 (1990), pp. 87–97
- S. Dempe, A necessary and a sufficient optimality condition for bilevel programming problems, Optimization, 25 (1992), pp. 341–354
- S. Dempe, A bundle algorithm applied to bilevel programming problems with non-unique lower level solutions, Computational Optimization and Applications, 15 (2000), pp. 145–166
- S. Dempe and J. Dutta, Is bilevel programming a special case of a mathematical program with complementarity constraints?, Mathematical Programming, 131 (2012), pp. 37–48
- J. E. Falk and J. Liu, On bilevel programming, part I: general nonlinear cases, Mathematical Programming, 70 (1995), pp. 47–72
- A. H. De Silva, Sensitivity formulas for nonlinear factorable programming and their application to the solution of an implicitly defined optimization model of U. S. crude oil production, phd thesis, George Washington University
- R. Lucchetti, F. Mignanego, and G. Pieri, Existence theorems of equilibrium points in stackelberg, Optimization, 18 (1987), pp. 857–866
- K. H. Sahin and A. R. Ciric, A dual temperature simulated annealing approach for solvingbilevel programming problems, Computers & chemical engineering, 23 (1998), pp. 11–25
- K. Shimizu and E. Aiyoshi, A new computational method for Stackelberg and min-max problems by use of a penalty method, IEEE Transactions on Automatic Control, 26 (1981),pp. 460–466
- H. Tuy, A. Migdalas, and N. Hoai-Phuong, A novel approach to bilevel nonlinear programming, Journal of Global Optimization, 38 (2007), pp. 527–554
- A. Yezza, First-order necessary optimality conditions for general bilevel programming problems, Journal of Optimization Theory and Applications, 89 (1996), pp. 189–219
