*--------------------------------------------------------------*
* Quadratically Constrained - Test Problem 4                   *
*--------------------------------------------------------------*
File  
    res  / results / ;
Put res ;

Sets
    i    /1*3/
    alias(i,j)
    alias(i,jp);

Parameters
    b(i)
    /1     3 
     2     0 
     3    -4/
    y(i)
    /1   1.5
     2  -0.5
     3    -5/
    z(i)
    /1     0
     2    -1
     3    -6/
    A(i,j);

Table A(i,j)
    1     2     3
1   0     0     1
2   0    -1     0
3  -2     1    -1;

Variables
    x(i)
    f;

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

x.up('1') = 2;
x.up('3') = 3;

Equations
    Obj    objective function
    Con1   constraint function 1
    Con2   constraint function 2
    Con3   constraint function 3;

Obj .. 
    f =e= -2*x('1') + x('2') - x('3');

Con1 ..
    sum(i, x(i)*sum(jp, A(jp,i)*sum(j, A(jp,j)*x(j)))) - 2*sum(i, y(i)*sum(j, A(i,j)*x(j)))
    + power(sqrt(sum(i, power(y(i),2))),2) - 0.25*power(sqrt(sum(i, power(b(i)-z(i),2))),2) =g= 0;

Con2 ..
    x('1') + x('2') + x('3') - 4 =l= 0;

Con3 ..
    3*x('2') + x('3') - 6 =l= 0;

Model
    problem /Obj, Con1, Con2, Con3/;

    x.l('1') = 0.5;
    x.l('2') = 0;
    x.l('3') = 3;

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