BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

mb_2007_02 : Linear-Linear problem from (Mitsos & Barton, 2007)

Optimal solution

Objective values Solution point(s)
Infeasible problem None

The inner problem is linear and has the unique optimal solution y = 1; however at this point the outer problem is infeasible and therefore the whole problem is also infeasible.

Illustration of the problem

Outer Problem Inner Problem

Sources where this problem occurs

Original source:

Other sources:

Description in the AMPL format

var y >= -1, <= 1;        # Inner variable(s)
var l{1..2} >= 0, <= 2;   # Multiplier(s)

minimize outer_obj: y;    # Outer objective

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

References