BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

Quadratic-Nonlinear bilevel problem from [Colson, 2002]


Optimal solution

Objective values Solution point
F* = 88.754 x* = 0.000
f* = -0.770 y* = 0.579

Sources where this problem occurs

Original source:

Other sources:

Description of the problem in the AMPL format

var x >= 0, <= 10;          # Outer variable
var y >= 0, <= 10;          # Inner variable
var l{1..3} >= 0, <= 100;   # KKT Multipliers

minimize outer_obj: x^2 + (y - 10)^2;  # Outer objective

subject to
# Outer constraints
    outer_con:  x + 2*y - 6 <= 0;
# Inner objective:
    inner_obj: x^3 + 2*y^3 + x - 2*y - x^2 = 0;
# Inner constraints
    inner_con:    -x + 2*y - 3 <= 0;
# KKT conditions:
    stationarity:      6*y^2 - 2 + 2*l[1] - l[2] + l[3] = 0;
    complementarity_1: l[1]*(-x + 2*y - 3) = 0;
    complementarity_2: l[2]*y = 0;
    complementarity_3: l[3]*(y - 10) = 0;

References