The OPTMODEL Procedure

The Rosenbrock Problem

You can use parameters to produce a clear formulation of a problem. Consider the Rosenbrock problem:

where is a parameter (constant), and are optimization variables (whose values are to be determined), and is an objective function.

Here is a PROC OPTMODEL program that solves the Rosenbrock problem:

    proc optmodel;
 
       number alpha = 100; /* declare parameter */
       var x {1..2};       /* declare variables */
 
       /* objective function */
       min f = alpha*(x[2] - x[1]**2)**2 +
               (1 - x[1])**2;
 
       /* now run the solver */
       solve;
       
       print x;
       quit;
 

The PROC OPTMODEL output is shown in Output 6.3.

The OPTMODEL Procedure Problem Summary Objective Sense Minimization Objective Function f Objective Type Nonlinear     Number of Variables 2 Bounded Above 0 Bounded Below 0 Bounded Below and Above 0 Free 2 Fixed 0     Number of Constraints 0 The OPTMODEL Procedure Solution Summary Solver L-BFGS Objective Function f Solution Status Optimal Objective Value 3.903434E-12 Iterations 8     Optimality Error 7.8875438E-6 [1] x 1 1 2 1

Figure 6.3: Rosenbrock Function Results