The Nonlinear Programming Solver

Consider the following larger optimization problem:

The problem consists of a quadratic objective function, 1,000 linear equality constraints, and a linear inequality constraint. There are also 2,005 variables. The goal is to find a local minimum by using the ACTIVESET technique. This can be accomplished by issuing the following call to PROC OPTMODEL:

proc optmodel;
   number n = 1000;
   number b = 5;
   var x{1..n} >= -1 <= 1 init  0.99;
   var y{1..n} >= -1 <= 1 init -0.99;
   var z{1..b} >=  0 <= 2 init  0.5;

   minimize f = sum{i in 1..n} x[i]*y[i] + 0.5*sum{j in 1..b} z[j]^2;
   con cons1{k in 1..n}: x[k] + y[k] + sum{j in 1..b} z[j] = b;
   con cons2: sum{i in 1..n} (x[i] + y[i]) + sum{j in 1..b} z[j] >= b + 1;

   solve with NLP / algorithm=activeset logfreq=10;
quit;

The SAS output displays a detailed summary of the problem along with the status of the solver at termination, the total number of iterations required, and the value of the objective function at the local minimum. The summaries are shown in Figure 5.

The SAS log shown in Figure 6 displays a brief summary of the problem that is being solved, followed by the iterations that are generated by the solver.