# ex003.mod
# Original AMPL coding by Sven Leyffer, University of Dundee
#
# A simple multi-objective optimization problem due to 
# Ravindra V. Tappeta and John E. Renaud, Dept. Aerospace & Mech. Engng.
# University of Notre Dame, "Interactive multiobjective optimization 
# procedure with local preferences", Proceedings of the 3rd WCSMO, 1999.

# ... sets & parameters
set I := 1..2;			# ... dimension of the problem

# ... variables
var x{I} >= 0;			# ... add bounds for MPEC

# ... objective functions
minimize  f1: (x[1] + x[2] - 7.5)^2 + 0.25*(x[2] - x[1] + 3)^2;
minimize  f2: 0.25*(x[1] - 1)^2  + 0.5*(x[2] - 4 )^2;

# ... constraints
subject to

   g1: 2.5 - 0.5*(x[1] - 2)^3 - x[2] >= 0;

   g2: 3.85 + 8*(x[2] - x[1] + 0.65)^2 - x[2] - x[1] >= 0;