A growing collection of bilevel problems
Nonlinear-Nonlinear bilevel problem from (Colson, 2002)
Objective values | Solution point |
---|---|
F* = 2.000 | x* = 4.000 |
f* = 24.018 | y* = 0.000 |
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 - 5)^4 + (2*y + 1)^4; # Outer objective
subject to
# Outer constraints
outer_con: x + y - 4 <= 0;
# Inner objective:
inner_obj: exp(-x+y) + x^2 + 2*x*y + y^2 + 2*x + 6*y = 0;
# Inner constraints
inner_con: -x + y - 2 <= 0;
# KKT conditions:
stationarity: exp(-x+y) + 2*x + 2*y + 6 + l[1] - l[2] + l[3] = 0;
complementarity_1: l[1]*(-x + y - 2) = 0;
complementarity_2: l[2]*y = 0;
complementarity_3: l[3]*(y - 10) = 0;