Quadratic-Quadratic bilevel problem from [Yezza, 1996]
Optimal solution
| Objective values | Solution points |
|---|---|
| F* = 1.5 | x* = 0.25 |
| f* = -2.5 | y* = 0.0 |
Sources where this problem occurs
Original source:
- Example 3.1 in (Yezza, 1996)
Other sources:
Description of the problem in the AMPL format
var x >= 0, <= 1; # Outer variable
var y >= 0, <= 1; # Inner variable
var l{1..5} >= 0, <= 10; # KKT Multipliers
minimize outer_obj: -(4*x - 3)*y + 2*x + 1; # Outer objective
subject to
# Inner objective:
inner_obj: -(1 - 4*x)*y - 2*x -2 = 0;
# KKT conditions:
stationarity: 4*x - 1 = 0;
complementarity_1: l[1]*y = 0;
complementarity_2: l[2]*(y - 1) = 0;
References
