# ex002.mod
# Original AMPL coding by Sven Leyffer, University of Dundee
#
# A simple multi-objective optimization problem due to 
# Jing-Fang Wang and John E. Renaud, Dept. Aerospace & Mech. Engng.
# University of Notre Dame, "Automatic differentiation in multi-
# objective collaborative optimization". 
# Proceedings of the 3rd WCSMO, 1999.
#
# NB: Mistake in paper; g2 should be y21 <= 10 (not >= 10)

# ... sets & parameters
set I := 1..3;			# ... dimension of the problem
param xl{I} default  0.0;	# ... lower bounds
param xu{I} default 10.0;	# ... upper bounds

# ... variables
var x{i in I} >= xl[i], <= xu[i];
var y12 >=  8;
var y21 <= 10;

# ... objective functions
minimize  f1: x[2]^2 + x[3] + y12;
minimize  f2: - y21 ;

# ... constraints
subject to

   def_y12: y12 = x[1]^2 + x[2] + x[3] - 0.2*y21;
   def_y21: y21 = x[1] + x[3] + sqrt( y12 );

# ... data statement & start points
data;
let xl[1] := -10.0;