Nonlinear-Nonlinear bilevel problem from (Colson, 2002)
Optimal solution
| Objective values | Solution point |
|---|---|
| F* = 227.691 | x* = 6.082 |
| f* = 0.000 | y* = 4.487 |
Sources where this problem occurs
Original source:
- BIPA1 in (Colson, 2002)
Other sources:
Description of the problem in the AMPL format
var x >= 0, <= 15; # Outer variable
var y >= 0, <= 20; # Inner variable
var l{1..3} >= 0, <= 100; # KKT Multipliers
minimize outer_obj: (10 - x)^3 + (10 - y)^3; # Outer objective
subject to
# Outer constraints
outer_con: -x + y <= 0;
# Inner objective:
inner_obj: (x + 2*y - 15)^4 = 0;
# Inner constraints
inner_con: x + y - 20 <= 0;
# KKT conditions:
stationarity: 8*(x + 2*y - 15)^3 + l[1] - l[2] + l[3] = 0;
complementarity_1: l[1]*(x + y - 20) = 0;
complementarity_2: l[2]*y = 0;
complementarity_3: l[3]*(y - 20) = 0;
References
