BASBLib - A Library of Bilevel Test Problems

A growing collection of bilevel problems

mb_2007_13v : Linear-Nonlinear problem, variation of mb_2007_13

Comments on the problem

This is a variation of mb_2007_13 problem. The only difference is the outer objective function, which is changed from x - y to x + y.

Optimal solution

Objective values Solution point(s)
F* = -2.000 x* = -1.000
f* = -1.500 y* = -1.000

Illustration of the problem

Outer Problem Inner Problem

Description in the AMPL format

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

minimize outer_obj: x + y;

subject to
# Inner objective:
    inner_obj: 0.5*x*y^2 - y*x^3 = 0;
# KKT conditions:
    stationarity:      x*y - x^3 - l[1] + l[2] = 0;
    complementarity_1: l[1]*(-1 - y) = 0;
    complementarity_2: l[2]*(y - 1) = 0;

References