quadratic programming problem with equality and inequality constraints

[rohailk]

hi,

I am trying to solve the following problem

and I have written the following code:

proc optmodel;
var x{1..3};
minimize f = x[1] - 2*x[2] + 4*x[3] + x[1]**2 + 2*x[2]**2 + 3*x[3]**2 + x[1]*x[2];

con r1: 3*x[1] + 4*x[2] -2*x[3] <= 10;
con r2: -3*x[1] + 2*x[2] + x[3] >= 2;
con r3: 2*x[1] + 3*x[2] + 4*x[3] =5;
con r4: x[1] <=5;
con r5: x[2] <=5;
con r6: x[3] <=5;
con r7: x[1] >=0;
con r8: x[2] >=0;
con r9: x[3] >=0;
solve with qp;
print x;
save qps qpsdata;
quit;

Please tell me if I am doing it right.Thanks

[RobPratt · Accepted solution]

Your code looks correct to me, but you can do it a little more simply by omitting the SAVE QPS statement and the WITH QP clause and by including the bounds in the VAR statement:

proc optmodel;
   var x{1..3} >= 0 <= 5;
   minimize f = x[1] - 2*x[2] + 4*x[3] + x[1]**2 + 2*x[2]**2 + 3*x[3]**2 + x[1]*x[2];

   con r1: 3*x[1] + 4*x[2] -2*x[3] <= 10;
   con r2: -3*x[1] + 2*x[2] + x[3] >= 2;
   con r3: 2*x[1] + 3*x[2] + 4*x[3] =5;
   solve;
   print x;
quit;

By using the EXPAND / SOLVE statement, you can see that both versions pass the same formulation to the solver.