Linear-Nonlinear bilevel problem from [Kleniati & Adjiman, 2014]
Optimal solution
| Objective values | Solution point(s) |
|---|---|
| F* = -1.000 | x* = 0.000 |
| f* = 0.000 | y* = 1.000 |
Illustration of the problem
| Outer Problem | Inner Problem |
|---|---|
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Description in the AMPL format
var x >= -1, <= 1; # Outer variables
var y >= -1, <= 1; # Inner variables
var l{1..2} >= 0, <= 2; # KKT Multipliers
minimize outer_obj: x - y;
subject to
# Inner objective:
inner_obj: 0.5*x*y^2 - x*y^3 = 0;
# KKT conditions:
stationarity: x*y - 3*x*y^2 - l[1] + l[2] = 0;
complementarity_1: l[1]*(-1 - y) = 0;
complementarity_2: l[2]*(y - 1) = 0;
References
