BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

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

Optimal solution

Objective values Solution point(s)
F* = 0.000 x* = -1.000
f* = -0.833 y* = 1.000

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

var x >= -1, <= 1;       # Outer variable
var y >= -1, <= 1;       # Inner variable
var l{1..2} >= 0, <= 2;  # Multipliers

minimize outer_obj: x + y;

subject to
# Inner objective
    inner_obj: 0.5*x*y^2 - y^3/3 = 0;
# KKT conditions
    stationarity:      x*y - y^2 - l[1] + l[2] = 0;
    complementarity_1: l[1]*(-1 - y) = 0;
    complementarity_2: l[2]*(y - 1) = 0;

References