The NLPC Nonlinear Optimization Solver

Iteration Log

The iteration log consists of one line of output containing the most important information for each iteration. The iteration log appears in the listing and can be captured as an ODS output data set. By default the iteration log is not displayed, but the user can use the PRINTFREQ= option to display it.

The following columns are common to all four optimization techniques. The words in parentheses indicate the column headings in long form; the words in angle brackets indicate the column headings in short form.

• iteration number (Iter)
• cumulative number of function calls, up to the end of the current iteration (Function Calls) <Func Calls>
• value of the objective function (Objective Value) <Obj Value>
• relative optimality error as described in the section "Optimality Control" (Optimality Error) <Optim Error>

The number displayed under the heading "Function Calls" does not include function calls performed during preprocessing. The number of function calls displayed by the PRINTLEVEL=2 option in the OPTMODEL procedure includes function calls performed in both preprocessing and postprocessing.

In addition to the preceding common columns, there are columns specific to an optimization technique, as follows.

• For the conjugate gradient (CONGRA) method, the following three additional columns are displayed:
  • step size (Step Size)
  • slope of the search direction, i.e., inner product of the gradients of the objective function and the search direction (Slope of Search Direction) <Slope Search Direc>
  • number of iteration restarts (Restarts) <Rest>
• For the Newton-type (NEWTYP) method, the following two additional columns are displayed:
  • step size (Step Size)
  • slope of the search direction (Slope of Search Direction) <Slope Search Direc>
• For the trust region (TRUREG) method, the following additional column is displayed:
  • trust region radius (Trust Region Radius)
• For the quasi-Newton (QUANEW) method, the columns displayed depend on whether the problem has nonlinear constraints or not. Without nonlinear constraints, the same two additional columns as in the Newton-type (NEWTYP) method are displayed. If there are nonlinear constraints, the following three additional columns are displayed:
  • relative infeasibility as described in the section "Infeasibility" (Infeasibility) <Infeas>
  • step size (Step Size)
  • predicted function reduction using the quadratic model (Predicted Function Reduction) <Pred Func Reduc>

Table 10.4 shows all the column headings that can appear in the ODS table "IterationLog," as well as the corresponding variable names in the ODS output data set.

Table 10.4: ODS Column Headings and Variable Names

Column Heading (Long)	Variable Name
Iter	Iter
Function Calls	Func
Objective Value	ObjVal
Optimality Error	MxGradRes
Step Size	Alpha
Slope of Search Direction	SlopeSD
Restarts	Rest
Trust Region Radius	Radius
Infeasibility	MxConViol
Predicted Function Reduction	PrFReduc

By default, the SAS list output is accumulated to a full page before it is displayed in the output window, so you do not see the iteration log immediately as the iteration proceeds. In order to view the iteration log immediately after every iteration, you need to set the AUTO SCROLL option to 1 in the SAS session. You can do this in either of the following two ways:

• Select a list output window. Then enter the command ascroll 1 in the command line window.
• In the output window, select Tools Options Preferences. In the Preferences window, click the Advanced tab and select Scroll lines from the Output group. Type 1 in the list box, and click OK to close the window.