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 x* = -1.000
f* = -1.000 y* = -1.000

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

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

minimize outer_obj: x;      # Outer objective

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

References