Quadratic-Quadratic bilevel problem from [Tuy et al., 2007]
Optimal solution
| Objective values | Solution points |
|---|---|
| F* = 22.5 | x* = 1.5 |
| f* = -4.5 | y* = 4.5 |
Sources where this problem occurs
Original source:
- Example 1 in (Tuy et al., 2007)
Other sources:
Description of the problem in the AMPL format
var x >= 0, <= 10; # Outer variable
var y >= 0, <= 10; # Inner variable
var l{1..5} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: x^2 + y^2; # Outer objective
subject to
# Inner objective:
inner_obj: -y = 0;
# Inner constraints
inner_con1: 3*x + y - 15 <= 0;
inner_con2: x + y - 7 <= 0;
inner_con3: x + 3*y - 15 <= 0;
# KKT conditions:
stationarity: -1 + l[1] + l[2] + 3*l[3] - l[4] + l[5] = 0;
complementarity_1: l[1]*(3*x + y - 15) = 0;
complementarity_2: l[2]*(x + y - 7) = 0;
complementarity_3: l[3]*(x + 3*y - 15) = 0;
complementarity_4: l[4]*y = 0;
complementarity_5: l[5]*(y - 10) = 0;
References
