BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

Linear-Nonlinear bilevel problem from [Mitsos & Barton, 2007]

Optimal solution

Objective values Solution point(s)
F* = -1.000 y* = -1.000
f* = -1.000  

The inner program has the unique optimal solution y = -1.0 and, therefore, the bilevel problem has the unique optimal solution y* = -1.0.

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

var y >= -1, <= 1;         # Inner variables
var l{1..2} >= 0, <= 10;   # KKT Multipliers

minimize outer_obj: y;    # Outer objective

subject to
# Inner objective:
    inner_obj: y^3 = 0;
# KKT conditions:
    stationarity:      3*y^2 - l[1] + l[2] = 0;
    complementarity_2: l[1]*(-1 - y) = 0;
    complementarity_3: l[2]*(y - 1) = 0;

References