Summary of NLP-NLP bilevel problems
Description of the Nonlinear-Nonlinear bilevel test problems: data and references
| Label | Source | n | m | F* | f* | x* | y* |
|---|---|---|---|---|---|---|---|
| c_2002_01 | (Colson, 2002) | 1 | 1 | 227.691 | 0.000 | 6.082 | 4.487 |
| c_2002_03 | (Colson, 2002) | 1 | 1 | 2.000 | 24.018 | 4.000 | 0.000 |
| c_2002_05 | (Colson, 2002) | 1 | 2 | 2.750 | 0.548 | 1.941 | (0.000, 1.211) |
| fz_1998_01 | (Floudas & Zlobec, 1998) | 1 | 2 | -1.000 | 1.000 | 1.000 | (0.000, 1.000) |
| mb_2007_24 | (Mitsos & Barton, 2007) | 2 | 3 | -2.350 | -2.000 | (-1.000, -1.000) | (1.000, 1.000, -0.707) |
| -2.350 | -2.000 | (-1.000, -1.000) | (1.000, -1.000, -0.707) | ||||
| nwj_2017_02 | (Nie et al., 2017) | 2 | 3 | -1.710 | -2.230 | (-1.000, -1.000) | (1.110, 0.310, -0.820) |
| nwj_2017_04 | (Nie et al., 2017) | 2 | 3 | -2.000 | -1.000 | (1.000, 1.000) | (0.000, 0.000, 1.000) |
| nwj_2017_03 | (Nie et al., 2017) | 4 | 4 | -0.437 | -1.190 | (0.000, 0.000, -0.707, -0.707) | (0.618, 0.000, -0.558, -0.554) |
| nwj_2017_05 | (Nie et al., 2017) | 4 | 4 | -0.437 | -1.190 | (0.000, 0.000, -0.707, -0.707) | (0.618, 0.000, -0.558, -0.554) |
| ka_2014_02 | (Kleniati & Adjiman, 2014) | 5 | 5 | -10.000 | -3.100 | (1.0, −1.0, −1.0, −1.0, −1.0) | (−1.0, −1.0, −1.0, −1.0, −1.0) |
References
- B. Colson, BIPA(BIlevel Programming with Approximation Methods)(software guide and test problems), Cahiers du GERAD, (2002)
- C. A. Floudas and S. Zlobec, Optimality and Duality in Parametric Convex Lexicographic Programming, Springer US, Boston, MA, 1998, pp. 359–379
- P.-M. Kleniati and C. S. Adjiman, Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part II: Convergence analysis and numerical results, Journal of Global Optimization, 60 (2014), pp. 459–481
- A. Mitsos and P. I. Barton, A Test Set for Bilevel Programs, 2007. Last updated September 19, 2007
- J. Nie, L. Wang, and J. Ye, Bilevel polynomial programs and semidefinite relaxation methods, SIAM Journal on Optimization, 27 (2017), pp. 1728–1757
