A growing collection of bilevel problems
Quadratic-Nonlinear bilevel problem from [Colson, 2002]
Objective values | Solution point |
---|---|
F* = 17.000 | x* = 1.000 |
f* = 2.000 | y* = 0.000 |
Original source:
Other sources:
AMPL
formatvar x >= 0, <= 10; # Outer variable
var y >= 0, <= 10; # Inner variable
var l{1..5} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: (x - 5)^2 + (2*y + 1)^2; # Outer objective
subject to
# Inner objective:
inner_obj: (y - 1)^2 - 1.5*x*y + x^3 = 0;
# Inner constraints
inner_con1: -3*x + y + 3 <= 0;
inner_con2: x - 0.5*y - 4 <= 0;
inner_con3: x + y - 7 <= 0;
# KKT conditions:
stationarity: 2*(y - 1) - 1.5*x + l[1] - 0.5*l[2] + l[3] - l[4] + l[5] = 0;
complementarity_1: l[1]*(-3*x + y + 3) = 0;
complementarity_2: l[2]*(x - 0.5*y -4) = 0;
complementarity_3: l[3]*(x + y -7) = 0;
complementarity_4: l[4]*y = 0;
complementarity_5: l[5]*(y - 10) = 0;