# bilevel1m.mod	QQR2-MN-8-7
# Original AMPL coding by Sven Leyffer, University of Dundee

# An MPEC from F. Facchinei, H. Jiang and L. Qi, A smoothing method for
# mathematical programs with equilibrium constraints, Universita di Roma
# Technical report, 03.96. Problem number 7

# Number of variables:   8
# Number of constraints: 7

var x{1..2} >= 0, <= 50;
var y{1..2};
var l{1..4};		# Multipliers

minimize f: 2*x[1] + 2*x[2] - 3*y[1] - 3*y[2] - 60;

subject to 

   c1: x[1] + x[2] + y[1] - 2*y[2] - 40 <= 0;
   F1: 0 = 2*y[1] - 2*x[1] + 40 - (l[1] - 2*l[3]);
   F2: 0 = 2*y[2] - 2*x[2] + 40 - (l[2] - 2*l[4]);

   m1: -10 <= y[1] <= 20         complements  l[1];
   m2: -10 <= y[2] <= 20         complements  l[2];
   g5: 0 <= x[1] - 2*y[1] - 10   complements  l[3] >= 0;
   g6: 0 <= x[2] - 2*y[2] - 10   complements  l[4] >= 0;