Quadratic-Quadratic bilevel problem from (Lucchetti et al., 1987)
Optimal solution
| Objective values | Solution point |
|---|---|
| F* = 0.0 | x* = 1.0 |
| f* = 0.0 | y* = 0.0 |
Sources where this problem occurs
Original source:
- Example 4.1 in (Lucchetti et al., 1987)
Other sources:
Description of the problem in the AMPL format
var x >= 0, <= 1; # Outer variables
var y >= 0, <= 1; # Inner variables
var l{1..2} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: 0.5*(1-x) + x*y;
subject to
# Inner objective
inner_obj: (x-1)*y = 0;
# KKT conditions
stationarity: x - 1 - l[1] + l[2] = 0;
complementarity_1: l[1]*y = 0;
complementarity_2: l[2]*(y - 1) = 0;
References
