Summary of QP-NLP bilevel problems
Description of the Quadratic-Nonlinear bilevel test problems: data and references
| Label | Source | n | m | F* | f* | x* | y* |
|---|---|---|---|---|---|---|---|
| mb_2007_12 | (Mitsos & Barton, 2007) | 1 | 1 | 0.000 | 0.000 | 0.000 | 0.000 |
| mb_2007_14 | (Mitsos & Barton, 2007) | 1 | 1 | 0.250 | -0.083 | 0.250 | 0.500 |
| mb_2007_17 | (Mitsos & Barton, 2007) | 1 | 1 | 0.188 | -0.016 | -0.250 | 0.500 |
| 0.188 | -0.016 | -0.250 | -0.500 | ||||
| mb_2007_18 | (Mitsos & Barton, 2007) | 1 | 1 | -1.000 | 0.000 | 1.000 | 0.000 |
| mb_2007_18v | [(Paulavicius et al., 2017b)][Paulavicius et al., 2017b] | 1 | 1 | 0.250 | 0.000 | 0.500 | 0.000 |
| mb_2007_19 | (Mitsos & Barton, 2007) | 1 | 1 | -0.258 | -0.018 | 0.189 | 0.439 |
| mb_2007_20 | (Mitsos & Barton, 2007) | 1 | 1 | 0.313 | -0.083 | 0.500 | 0.500 |
| mb_2007_21 | (Mitsos & Barton, 2007) | 1 | 1 | 0.210 | -0.069 | -0.555 | 0.455 |
| mb_2007_23 | (Mitsos & Barton, 2007) | 1 | 1 | -1.755 | 0.009 | 0.211 | 1.799 |
| mb_2007_22 | (Mitsos & Barton, 2007) | 1 | 1 | 0.189 | -0.042 | 0.635 | -0.433 |
| mb_2007_22v | [(Paulavicius et al., 2017b)][Paulavicius et al., 2017b] | 1 | 1 | 0.210 | -0.069 | -0.555 | 0.455 |
| dd_2012_01 | (Dempe & Dutta, 2012) | 1 | 1 | 1.000 | 0.000 | 0.000 | 0.000 |
| sib_1997_01 | (Shimizu et al., 1997) | 1 | 1 | 2250.000 | 194.800 | 11.250 | 5.000 |
| yz_2010_01 | (Ye & Zhu, 2010) | 1 | 1 | 1.000 | -2.000 | 1.000 | 1.000 |
| mb_2007_08 | (Mitsos & Barton, 2007) | 1 | 1 | 0.000 | 0.000 | -0.567 | 0.000 |
| c_2002_02 | (Colson, 2002) | 1 | 1 | 17.000 | 2.000 | 1.000 | 0.000 |
| c_2002_04 | (Colson, 2002) | 1 | 1 | 88.754 | -0.077 | 0.000 | 0.579 |
References
- B. Colson, BIPA(BIlevel Programming with Approximation Methods)(software guide and test problems), Cahiers du GERAD, (2002)
- 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
- A. Mitsos and P. I. Barton, A Test Set for Bilevel Programs, 2007. Last updated September 19, 2007
- R. Paulavičius, P.M. Kleniati, and C. S. Adjiman, BASBL: Branch-And-Sandwich BiLevel solver. II. Implementation and computational study with the BASBLib test set, (2017). Submitted.
- K. Shimizu, Y. Ishizuka, and J. F. Bard, Nondifferentiable and Two-Level Mathematical Programming, vol. 102, Kluwer Academic Publishers, Boston, 1997
- Ye, J. J., & Zhu, D. (2010). New necessary optimality conditions for bilevel programs by combining the MPEC and value function approaches. SIAM Journal on Optimization, 20(4), 1885-1905
