# AMPL Model by Hande Y. Benson
#
# Copyright (C) 2001 Princeton University
# All Rights Reserved
#
# Permission to use, copy, modify, and distribute this software and
# its documentation for any purpose and without fee is hereby
# granted, provided that the above copyright notice appear in all
# copies and that the copyright notice and this
# permission notice appear in all supporting documentation.                     

#   Source:  An idea by Nick Gould

#            Constrained optimization version

#   SIF input: Nick Gould, Nov 1992.

#   classification SQR2-AN-V-V

param m := 2;
param n := 2*m+1;

param a{j in 1..n, i in 1..j} := if (i == j) then m+1-j else
					if (i == j-1) then 1.0 else 0.0;

var d{1..n} := 1.0;
var q{i in 1..n, j in 1..n} := if (i==j) then 1.0;

minimize f:
	sum {j in 1..n, i in 1..j} (sum {k in 1..n} q[k,i]*q[k,j]*d[k] - a[j,i])^2; 

subject to cons{j in 1..n, i in 1..j: i != j}:
         sum {k in 1..n} q[k,i]*q[k,j] = 0.0;
subject to cons1{j in 1..n}:
         sum {k in 1..n} q[k,j]*q[k,j] = 1.0; 
solve;