# hs05x.mod
# AMPL coding by Sven Leyffer, University of Dundee.
#
# A simple multi-objective optimization problem (MOOP)
# constructed from Hock-Schittkowsky models hs051-hs053 
# of Bob Vanderbei's cute-ampl collection.

# ... sets & parameters
set I := 1..5;

# ... variables
var x{I} >= -10, <= 10;

# ... objective functions
minimize  f1: (  x[1]-x[2])^2 + (x[2]+x[3]-2)^2 + (2*x[4]-1)^2 + (  x[5]-1)^2;
minimize  f2: (4*x[1]-x[2])^2 + (x[2]-x[3]-2)^2 + (  x[4]-1)^2 + (3*x[5]-1)^2;
minimize  f3: (  x[1]+x[2])^2 + (x[2]+x[3]+2)^2 + (  x[4]+1)^2 + (  x[5]+1)^2;

# ... constraints
subject to

   c1: x[1] + 3*x[2]          = 4;
   c2: x[3] +   x[4] - 2*x[5] = 0;
   c3: x[2] -   x[5]          = 0;