Example 13.3 Solving a Bound-Constrained Optimization Problem

Consider the following optimization problem, where :

As you can see, this problem has variables. Also the first are allowed to take values only in the interval . In other words there are bounds on the values of the variables. Optimization problems that contain only this type of constraints are called bound-constrained problems. To solve the preceding problem you can use the following statements:

proc optmodel;
   number N=1000;
   var x{1..N} >=  - 1.5 <= 3.0;
   minimize f = sum {i in 1..N - 1} ( - 1.5 * x[i] + 2.5 * x[i + 1] +
      1.0 + (x[i] - x[i + 1])^2 + sin(x[i] + x[i + 1]));
   
   Solve with nlpu / tech=cgtr;
quit;

The optimal solution is displayed in Output 13.3.1.