* Cute AMPL model  (translation to GAMS)
*
* 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.

*   classification QLR2-AN-V-V

$Set nx 101
$Set ny 101

Set i /i0*i%nx%/;
Set j /j0*j%ny%/;


$Set nx1 i100
$Set ny1 j100

$Set nx2 i99
$Set ny2 j99


Set inside_i(i) /i1*i99/;
Set inside_j(j) /j1*j99/;

Set inside_1_i(i) /i1*i100/;
Set inside_1_j(j) /j1*j100/;

Set in_i(i) /i2*i99/;
Set in_j(j) /j2*j99/;

Variable     x[i,j],y[i,j],f ;

Equation Eq_1(i,j),Eq_2(i),Eq_3(i),Eq_4(j),Eq_5(j),Def_obj;


Eq_1(i,j)$((in_i(i)) and (in_j(j)))..
                     (x[i,j]    -  x[i-1,j])+ (y[i,j]     - y[i,j-1] )-1     =e= 0;

Eq_2(i)$(in_i(i))..
x[i,'j0']    + (x[i,'j1']   -  x[i-1,'j1'] ) + y[i,'j1']        -1 =e= 0;

Eq_3(i)$(in_i(i))..
x[i,'j%ny%'] + (x[i,'%ny1%']  -  x[i-1,'%ny1%']) - y[i,'%ny2%']-1=e= 0;

Eq_4(j)$(in_j(j))..
y['i0',j]    + (y['i1',j]   -  y['i1',j-1] ) + x['i1',j]        -1 =e= 0;
Eq_5(j)$(in_j(j))..
y['i%nx%',j] + (y['%nx1%',j]  -  y['%nx1%',j-1]) - x['%nx2%',j]-1=e= 0;


Def_obj.. f=e=
              (   sum{(i,j)$((inside_i(i)) and (inside_j(j))), sqr(x[i,j] -1)}
                + sum{(i,j)$((inside_i(i)) and (inside_j(j))), sqr(y[i,j] -1)}

                + sum{i$(inside_i(i)),sqr(x[i,'%ny1%'] - 1)}
                + sum{j$(inside_j(j)),sqr(y['%nx1%',j] - 1)}

        + sum {i$inside_1_i(i),  sqr(x[i,'j0'] - 1)    }
        + sum {i$inside_1_i(i),  sqr(x[i,'j%ny%'] - 1)  }
        + sum {j$inside_1_j(j),  sqr(y['i0',j] - 1)    }
        + sum {j$inside_1_j(j),  sqr(y['i%nx%',j] - 1)  }

              )
               / 2;

x.lo[i,'%ny1%']$inside_i(i) =1.0;
y.lo['%nx1%',j]$inside_j(j) =1.0;

Model aug2dc /all/;

Solve aug2dc using nlp minimize f;

display x.l;
display f.l;