*--------------------------------------------------------------*
* Quadratic Programming - Test Problem 10                      *
*--------------------------------------------------------------*
File  
    res  / results / ;
Put res ;

Sets     
    i    /1*10/
    j    /1*10/
    k    /1*10/;

Parameters
    lambda(j)
    /1    63 
     2    15
     3    44
     4    91
     5    45
     6    50
     7    89
     8    58 
     9    86
    10    82/
    mu(k)
    /1    42 
     2    98
     3    48
     4    91
     5    11
     6    63
     7    61
     8    61
     9    38
    10    26/
    alpha(j)
    /1   -19
     2   -27
     3   -23
     4   -53
     5   -42
     6    26
     7   -33
     8   -23
     9    41
    10    19/
    beta(k)
    /1   -52
     2    -3
     3    81
     4    30
     5   -85
     6    68
     7    27
     8   -81
     9    97
    10   -73/
    b(i)
    /1   380
     2   415
     3   385
     4   405
     5   470
     6   415
     7   400
     8   460
     9   400
    10   200/
    A1(i,j)
    A2(i,k);

Table A1(i,j)
    1     2     3     4     5     6     7     8     9    10
1   3     5     5     6     4     4     5     6     4     4
2   5     4     5     4     1     4     4     2     5     2
3   1     5     2     4     7     3     1     5     7     6
4   3     2     6     3     2     1     6     1     7     3
5   6     6     6     4     5     2     2     4     3     2
6   5     5     2     1     3     5     5     7     4     3
7   3     6     6     3     1     6     1     6     7     1
8   1     2     1     7     8     7     6     5     8     7
9   8     5     2     5     3     8     1     3     3     5
10  1     1     1     1     1     1     1     1     1     1;

Table A2(i,k)
    1     2     3     4     5     6     7     8     9    10
1   8     4     2     1     1     1     2     1     7     3
2   3     6     1     7     7     5     8     7     2     1
3   1     7     2     4     7     5     3     4     1     2
4   7     7     8     2     3     4     5     8     1     2
5   7     5     3     6     7     5     8     4     6     3
6   4     1     7     3     8     3     1     6     2     8
7   4     3     1     4     3     6     4     6     5     4
8   2     3     5     5     4     5     4     2     2     8
9   4     5     5     6     1     7     1     2     2     4
10  1     1     1     1     1     1     1     1     1     1;

Variables
    x(j)
    y(k)
    f;

Loop(j, 
    x.lo(j) = 0);

Loop(k, 
    y.lo(k) = 0);

Equations
    Obj     objective function
    Con(i)  constraint functions;

Obj .. 
    f =e= -0.5*sum(j, lambda(j)*power(x(j)-alpha(j),2))
        +  0.5*sum(k, mu(k)*power(y(k)-beta(k),2));

Con(i) ..
    sum(j, A1(i,j)*x(j)) + sum(k, A2(i,k)*y(k)) =l= b(i);

Model
    problem /Obj, Con/;

    x.l('1') = 0;
    x.l('2') = 0;
    x.l('3') = 0;
    x.l('4') = 0;
    x.l('5') = 0;
    x.l('6') = 4.348;
    x.l('7') = 0;
    x.l('8') = 0;
    x.l('9') = 0;
    x.l('10') = 0;

    y.l('1') = 0;
    y.l('2') = 0;
    y.l('3') = 0;
    y.l('4') = 62.609;
    y.l('5') = 0;
    y.l('6') = 0;
    y.l('7') = 0;
    y.l('8') = 0;
    y.l('9') = 0;
    y.l('10') = 0;

    solve problem using nlp minimizing f;
    PUT "Min f",f.l:16:10//;
    Loop(j, PUT "x   ",x.l(j):16:10//);
    Loop(k, PUT "y   ",y.l(k):16:10//);