A growing collection of bilevel problems
Quadratic-Quadratic bilevel problem from [Bard, 1998]
Objective values | Solution points |
---|---|
F* = 0.000 | x* = (1.000, 0.400) |
f* = -0.320 | y* = 0.800 |
AMPL
formatvar x{1..2} >= 0, <= 1; # Outer variable
var y >= 0, <= 1; # Inner variable
var l{1..2} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: 0.5*(x[1] - 1)^2 + 0.5*(x[2] - 0.4)^2 + 0.5*(y - 0.8)^2; # Outer objective
subject to
# Inner objective:
inner_obj: 0.5*y^2 - y + (-1)*x[1]*y + 3*x[2]*y = 0;
# KKT condition
stationarity: y - 1 - x[1] + 3*x[2] - l[1] + l[2] = 0;
complementarity_1: l[1]*y = 0;
complementarity_2: l[2]*(y - 1) = 0;