quadratic_bilevel

Datasets

aiyoshi_shimizu_1984_ex2.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 5, "H": 0, "f": 1, "g": 6, "h": 0 }

Solution

{ "optimality": "global", "x": [25,30], "y": [5,10], "F": 65, "G": [0,25,30,25,20], "H": [], "f": -800, "g": [5,0,15,20,15,10], "h": [] }

an_et_al_2009.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 6, "h": 0 }

Solution

{ "optimality": "global", "x": [0.2,2], "y": [4,4.6], "F": 2231.727818, "G": [0,0,0.2,2], "H": [], "f": 565.774477, "g": [0,0,0,0,4,4.6], "h": [] }

bard_1988_ex1.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 1, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [1], "y": [0], "F": -9, "f": 0 }

bard_1988_ex2.json

Dimension

{ "x": 4, "y": 4, "F": 1, "G": 9, "H": 0, "f": 1, "g": 12, "h": 0 }

Solution

{ "optimality": "unknown" }

bard_1991_ex1.json

Dimension

{ "x": 1, "y": 2, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [2], "y": [6,0], "F": 2, "G": [0,2], "f": 12, "g": [0,6,0] }

bard_book_1998.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 7, "h": 0 }

Solution

{ "optimality": "global", "x": [25,30], "y": [5,10], "F": -800, "G": [25,30,25,20], "f": 65, "g": [0,5,0,15,20,15,10] }

calamai_vicente_1994a.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [1.25], "y": [0.25], "F": -0.4375, "G": [], "f": -0.1875, "g": [0,0.5,0] }

calamai_vicente_1994b.json

Dimension

{ "x": 4, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 6, "h": 0 }

Solution

{ "optimality": "global", "x": [1.25,0.5,1,1], "y": [0.25,0.5], "F": -1.6875, "G": [], "f": -0.40625, "g": [0,1,0,2,0.5,0] }

calamai_vicente_1994c.json

Dimension

{ "x": 4, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 6, "h": 0 }

Solution

{ "optimality": "global", "x": [0.13085,0.05195,0.1022,0.0674], "y": [0.025,0.05], "F": -1.6875, "G": [], "f": -0.40625, "g": [0,1,0,2,0.5,0] }

clark_westerberg_1990a.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [1], "y": [3], "F": -8, "G": [7,1], "f": -21, "g": [0,3,7] }

dempe_etal_2012.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [-1], "y": [1], "F": -1, "G": [0,2], "f": -1, "g": [1,0] }

dempe_franke_2011_ex41.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [0,-1], "y": [1,2], "F": 5, "G": [1,0,1,2], "f": -2, "g": [0,1,0,2] }

dempe_franke_2011_ex42.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [1,-1], "y": [0,1], "F": 2, "G": [2,0,0,2], "f": -1, "g": [0,2.5,1] }

dempe_franke_2014_ex38.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [-1,-1], "y": [2,2], "F": -1, "G": [0,0,2,0.25], "f": -4, "g": [2,2,0,0] }

dempe_lohse_2011_ex31a.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [0,0], "y": [1,1], "F": -6, "G": [], "f": 0, "g": [0,0,1,1] }

dempe_lohse_2011_ex31b.json

Dimension

{ "x": 3, "y": 3, "F": 1, "G": 0, "H": 0, "f": 1, "g": 5, "h": 0 }

Solution

{ "optimality": "unknown", "x": [0.5,0.5,0], "y": [0,0,2], "F": -12.5, "G": [], "f": 0, "g": [0,0,0,0,2] }

desilva_1978.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [0.5,0.5], "y": [0.5,0.5], "F": -1, "G": [], "f": 0, "g": [0,0,1,1] }

falk_liu_1995.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [0.8660254037844386,0.8660254037844386], "y": [0.8660254037844386,0.8660254037844386], "F": -2.1961524227066325, "G": [], "f": 0, "g": [0.3660254037844386,0.3660254037844386,0.6339745962155614,0.6339745962155614] }

floudas_etal_2013.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 4, "H": 0, "f": 1, "g": 7, "h": 0 }

Solution

{ "optimality": "global", "x": [0,0], "y": [-10,-10], "F": 60, "G": [0,0,50,50], "f": -600, "g": [10,10,30,0,0,30,30] }

gumus_floudas_2001_ex.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 5, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [3], "y": [5], "F": -4, "G": [2,5,1,3,5], "f": -25, "g": [5,5] }

hatz_etal_2013.json

Dimension

{ "x": 1, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [0], "y": [0,0], "F": 0, "G": [], "f": 0, "g": [0,0] }

henderson_quandt_1958.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 1, "h": 0 }

Solution

{ "optimality": "best_known", "x": [93.33333333], "y": [26.66666667], "F": -3266.6666665499997, "G": [93.33333333,106.66666667], "f": -711.1111111555551, "g": [26.66666667] }

henrion_surowiec_2011.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 0, "h": 0 }

Solution

{ "optimality": "global", "x": [-0.5], "y": [-0.5], "F": -0.25, "G": [], "f": -0.125, "g": [] }

lampariello_sagratella_2017_ex31.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 1, "H": 0, "f": 1, "g": 1, "h": 0 }

Solution

{ "optimality": "global", "x": [1], "y": [0], "F": 1, "G": [0], "f": 0, "g": [0] }

lampariello_sagratella_2017_ex32.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 0, "h": 0 }

Solution

{ "optimality": "global", "x": [0.5], "y": [0.5], "F": 0.5, "G": [], "f": -1, "g": [] }

lampariello_sagratella_2017_ex33.json

Dimension

{ "x": 1, "y": 2, "F": 1, "G": 1, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [0.5], "y": [0.5,0], "F": 0.5, "G": [0], "f": 0.5, "g": [0,0.5,0] }

lampariello_sagratella_2017_ex35.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [0.8], "y": [0.4], "F": 0.8, "G": [1.8,0.2], "f": -0.4, "g": [0,0.4,0.6] }

lucchetti_etal_1987.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [1], "y": [0], "F": -0.5, "G": [1,0], "f": 0, "g": [0,1] }

macal_hurter_1997.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 0, "h": 0 }

Solution

{ "optimality": "global", "x": [10.0163], "y": [0.8197], "F": 79.32617377999999, "G": [], "f": -0.3321014549999859, "g": [] }

morgan_patrone_2006a.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [0], "y": [1], "F": -1, "G": [0.5,0.5], "f": 0, "g": [2,0] }

muu_quy_2003_ex1.json

Dimension

{ "x": 1, "y": 2, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "best_known", "x": [0.8438], "y": [0.7657,0], "F": -2.07690507, "G": [0.8438,1.1562000000000001], "f": -0.5862964900000003, "g": [1.1562,0.7657,0] }

muu_quy_2003_ex2.json

Dimension

{ "x": 2, "y": 3, "F": 1, "G": 3, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "best_known", "x": [0.609,0.391], "y": [0,0,1.828], "F": 0.642584, "G": [0,0.609,0.391], "f": 1.670792, "g": [0.001,0,0,1.828] }

outrata_1990_ex1_a.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "infeasible", "x": [0.97,3.14], "y": [2.6,1.8], "F": -8.91995, "G": [], "f": -6.053999999999999, "g": [1.0658,-0.0005999999999999339,2.6,1.8] }

outrata_1990_ex1_b.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "best_known", "x": [0.28,0.48], "y": [2.34,1.03], "F": -7.562950000000001, "G": [], "f": -0.5799499999999999, "g": [1.74922,0.002990000000000048,2.34,1.03] }

outrata_1990_ex1_c.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "infeasible", "x": [20.26,42.81], "y": [3,3], "F": -12, "G": [], "f": -112.71000000000001, "g": [-0.0009999999999998899,-0.0009999999999998899,3,3] }

outrata_1990_ex1_d.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "best_known", "x": [2,0.06], "y": [2,0], "F": -3.59964, "G": [], "f": -2, "g": [2.666,0,2,0] }

outrata_1990_ex1_e.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 0, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "best_known", "x": [2.42,-3.65], "y": [0,1.58], "F": -3.15391, "G": [], "f": -16.2898, "g": [0.41999999999999993,2.52614,0,1.58] }

outrata_cervinka_2009.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 1, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [0,0], "y": [0,0], "F": 0, "G": [0], "f": 0, "g": [0,0,0] }

sahin_ciric_1998_ex2.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [1], "y": [3], "F": -8, "G": [1,7], "f": -21, "g": [0,3,7] }

shimizu_aiyoshi_1981_ex1.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 3, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [10], "y": [10], "F": 0, "G": [0,10,5], "f": -900, "g": [0,10,10] }

shimizu_aiyoshi_1981_ex2.json

Dimension

{ "x": 2, "y": 2, "F": 1, "G": 3, "H": 0, "f": 1, "g": 4, "h": 0 }

Solution

{ "optimality": "global", "x": [20,5], "y": [10,5], "F": -1075, "G": [0,0,10], "f": 100, "g": [10,5,0,5] }

shimizu_etal_1997a.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "global", "x": [5], "y": [2], "F": -1, "G": [], "f": -15, "g": [10,0,0] }

sinha_malo_deb_2014_tp6.json

Dimension

{ "x": 1, "y": 2, "F": 1, "G": 1, "H": 0, "f": 1, "g": 6, "h": 0 }

Solution

{ "optimality": "unknown", "x": [0], "y": [0,0], "F": 0, "G": [0], "f": 0, "g": [12,-4,4,4,0,0] }

toll_setting_p1.json

Dimension

{ "x": 3, "y": 8, "F": 1, "G": 3, "H": 0, "f": 1, "g": 18, "h": 0 }

Solution

{ "optimality": "best_known", "x": [7,4,6], "y": [0,0,1,0,0,0,0,0], "F": -7, "G": [7,4,6], "f": 12, "g": [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0] }

toll_setting_p2.json

Dimension

{ "x": 3, "y": 18, "F": 1, "G": 3, "H": 0, "f": 1, "g": 38, "h": 0 }

Solution

{ "optimality": "best_known", "x": [0.5,4,4.5], "y": [0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1], "F": -4.5, "G": [0.5,4,4.5], "f": 32, "g": [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1] }

toll_setting_p3.json

Dimension

{ "x": 3, "y": 18, "F": 1, "G": 3, "H": 0, "f": 1, "g": 38, "h": 0 }

Solution

{ "optimality": "best_known", "x": [5,3.5,8.5], "y": [0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,1], "F": -3.5, "G": [5,3.5,8.5], "f": 32, "g": [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,1] }

toll_setting_p4.json

Dimension

{ "x": 2, "y": 4, "F": 1, "G": 0, "H": 0, "f": 1, "g": 8, "h": 0 }

Solution

{ "optimality": "best_known", "x": [2.5,-1], "y": [0,1,1,0], "F": -4, "G": [], "f": 14, "g": [0,0,0,0,0,1,1,0] }

toll_setting_p5.json

Dimension

{ "x": 1, "y": 4, "F": 1, "G": 0, "H": 0, "f": 1, "g": 8, "h": 0 }

Solution

{ "optimality": "best_known", "x": [2.5], "y": [0,1,0,1], "F": -2.5, "G": [], "f": 14, "g": [0,0,0,0,0,1,0,1] }

tuy_etal_2007.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 3, "h": 0 }

Solution

{ "optimality": "infeasible", "x": [4.492188], "y": [1.523438], "F": 22.500616367187995, "G": [4.492188,1.523438], "f": -1.523438, "g": [-0.000002000000000279556,0.9843740000000007,5.9374980000000015] }

wan_wang_lv_2011.json

Dimension

{ "x": 2, "y": 3, "F": 1, "G": 0, "H": 0, "f": 1, "g": 8, "h": 0 }

Solution

{ "optimality": "global", "x": [0,0.75], "y": [0,0.5,0], "F": 2.625, "G": [], "f": -0.5, "g": [0.5,0,0,0,0.75,0,0.5,0] }

yezza_1996_ex3.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 2, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "global", "x": [0.25], "y": [0], "F": 0.5, "G": [0.25,0.75], "f": -0.5, "g": [0,1] }

yezza_1996_ex4.json

Dimension

{ "x": 1, "y": 1, "F": 1, "G": 0, "H": 0, "f": 1, "g": 2, "h": 0 }

Solution

{ "optimality": "unknown", "x": [3], "y": [1], "F": -3.5, "G": [], "f": 2.5, "g": [1,2] }