A growing collection of bilevel problems
Linear-Quadratic bilevel problem from [Bard, 1991]
Objective values | Solution points |
---|---|
F* = 2.000 | x* = 2.000 |
f* = 12.000 | y* = (6.000, 0.000) |
Original source:
Other sources:
AMPL
formatvar x >= 2, <= 4; # Outer variable
var y{1..2} >= 0, <= 10; # Inner variable
var l{1..5} >= 0, <= 100; # KKT Multipliers
minimize outer_obj: x + y[2]; # Outer objective
subject to
# Inner objective:
inner_obj: 2*y[1] + x*y[2] = 0;
# Inner constraints
inner_con: x - y[1] - y[2] + 4 <= 0;
# KKT conditions:
stationarity_1: 2 - l[1] - l[2] + l[3] = 0;
stationarity_2: x - l[1] - l[4] + l[5] = 0;
complementarity_1: l[1]*(x - y[1] - y[2] + 4) = 0;
complementarity_4: l[2]*y[1] = 0;
complementarity_5: l[3]*(y[1] - 10) = 0;
complementarity_6: l[4]*y[2] = 0;
complementarity_7: l[5]*(y[2] - 10) = 0;