A growing collection of bilevel problems
Quadratic-Nonlinear bilevel problem from [Colson, 2002]
Objective values | Solution point |
---|---|
F* = 88.754 | x* = 0.000 |
f* = -0.770 | y* = 0.579 |
Original source:
Other sources:
AMPL
formatvar x >= 0, <= 10; # Outer variable
var y >= 0, <= 10; # Inner variable
var l{1..3} >= 0, <= 100; # KKT Multipliers
minimize outer_obj: x^2 + (y - 10)^2; # Outer objective
subject to
# Outer constraints
outer_con: x + 2*y - 6 <= 0;
# Inner objective:
inner_obj: x^3 + 2*y^3 + x - 2*y - x^2 = 0;
# Inner constraints
inner_con: -x + 2*y - 3 <= 0;
# KKT conditions:
stationarity: 6*y^2 - 2 + 2*l[1] - l[2] + l[3] = 0;
complementarity_1: l[1]*(-x + 2*y - 3) = 0;
complementarity_2: l[2]*y = 0;
complementarity_3: l[3]*(y - 10) = 0;