purpose of FIX command in proc optmodel for solving non linear optimization problem

[rohailk]

hi,

I am trying to solve the following problem

I mean I want to minimize the function f(x).

I have written the following code (without the FIX commands)

proc optmodel;
var x1, x2 , x3;
min f = x1^2 + 2*(x2^2) + 5*(x3^2) -4*x1 -20*x2 -20*x3;
/* starting point */
x1 = 0;
x2 = 0;
x3 = 0;
solve; 
print x1 x2 x3 x1.dual x2.dual x3.dual;
quit;

and I get the following result

There are no values for the dual but I get the value of objective function

But when I write the same code with fix commands (as given below).

proc optmodel;
var x1, x2 , x3;
min f = x1^2 + 2*(x2^2) + 5*(x3^2) -4*x1 -20*x2 -20*x3;
/* starting point */
fix x1 = 0;
fix x2 = 0;
fix x3 = 0;
solve; 
print x1 x2 x3 x1.dual x2.dual x3.dual;
quit;

then i get the following result

+

now there are no values for the 3 variables and also no value for the objective function

Sorry I dont know exactly the function of "FIX" command.

Please can you explain the purpose of "FIX" command here.

Which code should I use to solve this problem?

thanks

[RobPratt · Accepted solution]

The FIX statement fixes variables to the specified values.  If you want to minimize the function, don't fix anything, and the solver will find optimal values for the variables.  At a locally optimal solution, the dual values will be 0.  But to find the gradient at a given solution, you must fix the variables.  The resulting dual values (gradient) indicate the direction of steepest descent.  As you did in other questions, you would proceed with a line search to find the best step length alpha in that direction.