The Nonlinear Programming Solver

Consider the following optimization problem:

The objective function is highly nonlinear and contains many local minima. The NLP solver provides you with the option of searching the feasible region and identifying local minima of better quality. This is achieved by writing the following SAS program:

proc optmodel;
  var x >= -1 <= 1;
  var y >= -1 <= 1;
  min f = exp(sin(50*x)) + sin(60*exp(y)) + sin(70*sin(x)) + sin(sin(80*y)) 
          - sin(10*(x+y)) + (x^2+y^2)/4;
  solve with nlp / multistart seed=94245 msmaxstarts=30;
quit;   

The MULTISTART option is specified, which directs the algorithm to start the local solver from many different starting points. The SAS log is shown in Figure 8.5.

The SAS log presents additional information when the MULTISTART option is enabled. The first column counts the number of restarts of the local solver. The second column records the best local optimum that has been found so far, and the third through sixth columns record the local optimum to which the solver has converged. The final column records the status of the local solver at every iteration.

The SAS output is shown in Figure 8.6.