# liswetx.mod
# AMPL coding by Sven Leyffer, University of Dundee.
#
# A simple multi-objective optimization problem (MOOP)
# constructed from models liswet1-liswet4
# of Bob Vanderbei's cute-ampl collection.
#
# removed silly constant in objective.

# ... parameters
param n:=5;
param k:=2;
set 0k  := 0..k;
set 1n  := 1..n;
set 1nk := 1..n+k;
param B{i in 0k} := if (i=0) then 1 else B[i-1]*i;
param C{i in 0k} := if (i=0) then 1 else (-1)^i*B[k]/(B[i]*B[k-i]);
param T{i in 1nk} := (i-1)/(n+k-1);

# ... variables
var x{1nk} := 0.0;

# ... objective functions
minimize f1: 	sum {i in 1nk} -(sqrt(T[i])+0.1*sin(i))*x[i] + 
		sum {i in 1nk} 0.25*x[i]^2;

minimize f2:	sum {i in 1nk} -(T[i]^3+0.1*sin(i))*x[i] +
		sum {i in 1nk} 0.5*x[i]^2;

subject to 

	c1{j in 1n}: sum {i in 0k} C[i]*x[j+k-i] >= 0;