A growing collection of bilevel problems
Quadratic-Quadratic bilevel problem from (Dempe, 1992)
Objective values | Solution points |
---|---|
F* = 31.25 | x* = 1.0 |
f* = 4.00 | y* = 1.0 |
Original source:
Other sources:
AMPL
formatvar x >= 1, <= 10; # Outer variables
var y >= 1, <= 10; # Inner variables
var l{1..3} >= 0, <= 100; # KKT Multipliers
minimize outer_obj: (x - 3.5)^2 + (y + 4)^2; # d > 0 fixed, so we use d = 1
subject to
# Inner objective
inner_obj: (y - 3)^2 = 0;
# Inner constraints
inner_con: y^2 - x <= 0;
# KKT conditions
stationarity: 2*(y - 3) + 2*y*l[1] - l[2] + l[3] = 0;
complementarity_1: l[1]*(y^2 - x) = 0;
complementarity_2: l[2]*(-y - 1) = 0;
complementarity_3: l[3]*(y - 10) = 0;