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Example 13.5: Unconstrained NLP Optimization

The SQP solver is designed mainly for constrained optimization problems, but it can be used for solving unconstrained optimization problems as well. Consider the following example:

Assume the starting point . You can use the following SAS code to solve the problem:

    proc optmodel;
       var x init 0;   /* starting point */
       
       minimize obj =  
          sin(x) + cos(x);
       
       solve with sqp/ printfreq = 0;
       print x;
    quit;
 

The optimal solution is displayed in Output 13.5.1.

You can also solve the same function by using the NLPU solver for unconstrained NLP problems. The SAS code is as follows:

    proc optmodel;
       var x init 0;   /* starting point */
       
       minimize obj =  
          sin(x) + cos(x);
       
       solve;  /* the default solver is NLPU */
       print x;
    quit;
 

The optimal solution is displayed in Output 13.5.2.

The L-BFGS method is the default technique used in the NLPU solver when a nonlinear programming problem with no variable bounds is specified. See Chapter 11, "The Unconstrained Nonlinear Programming Solver," for details.