BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

mb_2007_18v : Quadratic-Nonlinear problem, variation of mb_2007_18

Comments on the problem

This is a variation of mb_2007_18 problem. The only difference is the outer objective function, which is changed from -x^2 + y^2 to x^2 + y^2.

Optimal solution

Objective values Solution point(s)
F* = 0.250 x* = 0.500
f* = 0.000 y* = 0.000

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

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

minimize outer_obj: x^2 + y^2;

subject to
# Inner objective
    inner_obj: x*y^2 - y^4/2 = 0;
# KKT conditions
    stationarity:      2*x*y - 2*y^3 - l[1] + l[2] = 0;
    complementarity_1: l[1]*(-1 - y) = 0;
    complementarity_2: l[2]*(y - 1) = 0;

References