BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

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

Optimal solution

Objective values Solution point(s)
F* = 0.250 x* = 0.250
f* = -0.083 y* = 0.500

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

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

minimize outer_obj: (x - 0.25)^2 + y^2;

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

References