A growing collection of bilevel problems
Quadratic-Quadratic bilevel problem from [Bard, 1998]
Objective values | Solution points |
---|---|
F* = 81.33 | x* = 10.02 |
f* = -0.336 | y* = 0.82 |
AMPL
formatvar x >= -100, <= 100; # Outer variable
var y >= -100, <= 100; # Inner variable
var l{1..2} >= 0, <= 1000; # KKT Multipliers
minimize outer_obj: (x - 1)^2 + (y - 1)^2; # Outer objective
subject to
# Inner objective:
inner_obj: 0.5*y^2 + 500*y - 50*x*y = 0;
# KKT condition
stationarity: y + 500 - 50*x - l[1] + l[2] = 0;
complementarity_1: l[1]*(-y - 100) = 0;
complementarity_2: l[2]*(y - 100) = 0;