mb_2006_01 : Linear-Quadratic bilevel problem from [Mitsos & Barton, 2006]

---

Optimal solution

Objective values	Solution point(s)
F* = -1.000	y* = -1.000
f* = -1.000

Illustration of the problem

Outer Problem	Inner Problem

Sources where this problem occurs

Original source:

• Example 4.2 in (Mitsos & Barton, 2006)

Other sources:

Description in the AMPL format

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

# OUTER OBJECTIVE
minimize outer_obj: y;   # Outer objective

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

References

• A. Mitsos and P. I. Barton, Issues in the development of global optimization algorithms for bilevel programs with a nonconvex inner program, Technical report, Massachusetts Institute of Technology