BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

Quadratic-Quadratic bilevel problem from [Bard, 1998]


Optimal solutions

Objective values Solution points
F* = 81.33 x* = 10.02
f* = -0.336 y* = 0.82

Description of the problem in the AMPL format

var x >= -100, <= 100;      # Outer variable
var y >= -100, <= 100;      # Inner variable
var l{1..2} >= 0, <= 1000;  # KKT Multipliers

minimize outer_obj: (x - 1)^2 + (y - 1)^2;  # Outer objective

subject to
# Inner objective:
    inner_obj: 0.5*y^2 + 500*y - 50*x*y = 0;
# KKT condition
    stationarity:      y + 500 - 50*x - l[1] + l[2] = 0;
    complementarity_1: l[1]*(-y - 100) = 0;
    complementarity_2: l[2]*(y - 100) = 0;

References