A growing collection of bilevel problems
Linear-Nonlinear bilevel problem from (Gümüş & Floudas, 2001)
Objective values | Solution point |
---|---|
F* = 0.19 | x* = 0.194 |
f* = -7.25 | y* = (9.97, 10.0) |
Original source:
Other sources:
AMPL
formatvar x >= 0.1, <= 10; # Outer variables
var y{1..2} >= 0.1, <= 10.0001; # Inner variables
var l{1..6} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: x; # Outer objective
subject to
# Inner objective:
inner_obj: -y[1] + 0.5864*y[1]^(2/3) = 0;
# Inner constraints
inner_con1: 0.0332333/y[2] + 0.1*y[1] -1 <= 0;
inner_con2: 4*x/y[2] + 2*x^(-0.71)/y[2] + 0.0332333*x^(-1.3) - 1 <= 0;
# KKT conditions:
stationarity_1: -1 + 0.5864*(2/3)*y[1]^(-1/3) + 0.1*l[1] - l[3] + l[4] = 0;
stationarity_2: -l[1]*0.0332333/y[2]^2 - l[2]*(4*x/y[2]^2 + 2*x^(-0.71)/y[2]^2) - l[5] + l[6] = 0;
complementarity_1: l[1]*(0.0332333/y[2] + 0.1*y[1] -1) = 0;
complementarity_2: l[2]*(4*x/y[2] + 2*x^(-0.71)/y[2] + 0.0332333*x^(-1.3) - 1) = 0;
complementarity_3: l[3]*(0.1 - y[1]) = 0;
complementarity_4: l[4]*(y[1] - 10) = 0;
complementarity_5: l[5]*(0.1-y[2]) = 0;
complementarity_6: l[6]*(y[2]-10) = 0;