Displayed Output
Procedure Initialization
After the procedure has processed the problem, it displays
summary information about the problem and the options that
you have selected.
It may also display a list of linearly dependent constraints
and other information about the constraints and parameters.
Optimization Start
At the start of optimization the procedure displays
- the number of constraints that are active at the
starting point, or more precisely, the number of
constraints that are currently members of the
working set.
If this number is followed by a plus
sign, there are more active constraints, of which
at least one is temporarily released from the working
set due to negative Lagrange multipliers
- the value of the objective function at the starting point
- if the (projected) gradient is available, the value
of the largest absolute (projected) gradient element
- for the TRUREG and LEVMAR subroutines, the initial radius
of the trust region around the starting point
Iteration History
In general, the iteration history consists of one line of
output containing the most important information
for each iteration. The iteration-extensive Nelder-Mead
simplex method, however, displays only one line for several
internal iterations. This technique skips the output
for some iterations because
- some of the termination tests (size and standard deviation)
are rather timeconsuming compared to the simplex
operations and are only done every five simplex
operation.
- the resulting history output is smaller
The _LIST_ variable (refer to the "Program Statements" section)
also enables you to display the parameter estimates
x(k) and the gradient g(k) in all or some selected
iterations k.
The iteration history always includes the following
(the words in parentheses indicate the column header output):
- the iteration number (iter)
- the number of iteration restarts (nrest)
- the number of function calls (nfun)
- the number of active constraints (act)
- the value of the optimization criterion (optcrit)
- the difference between adjacent function values (difcrit)
- the maximum of the absolute (projected) gradient
components (maxgrad)
An apostrophe trailing the number of active constraints indicates
that at least one of the active constraints was released from the
active set due to a significant Lagrange multiplier.
The optimization history is displayed by default because it is
important to check for possible convergence problems.
Optimization Termination
The output of the optimization history ends with a short
output of information concerning the optimization result:
- the number of constraints that are active at the
final point, or more precisely, the number of
constraints that are currently members of the
working set
When this number is followed by a plus sign,
it indicates that there are more active
constraints of which at least one is temporarily
released from the working set due to negative
Lagrange multipliers.
- the value of the objective function at the final point
- if the (projected) gradient is available, the value
of the largest absolute (projected) gradient element
- other information that is specific for the optimization
technique
The NOPRINT option suppresses all output to the
list file and only error's, warning's, and note's are
displayed to the log file. The PALL option sets a large
group of some of the commonly used specific displaying options,
the PSHORT option suppresses some, and the PSUM (or PSUMMARY)
option suppresses almost all of the default output. The
following table summarizes the correspondence between
the general and the specific print options
| Output Options | PALL | default | PSHORT | PSUM | |
| | y | y | y | y | summary of optimization |
| | y | y | y | n | parameter estimates |
| | y | y | y | n | gradient of objective func |
| PHISTORY | y | y | y | n | iteration history |
| PINIT | y | y | n | n | setting of initial values |
| | y | y | n | n | listing of constraints |
| PGRID | y | n | n | n | results of grid search |
| PNLCJAC | y | n | n | n | Jacobian nonlin. constr. |
| PFUNCTION | y | n | n | n | values of functions |
| PEIGVAL | y | n | n | n | eigenvalue distribution |
| PCRPJAC | y | n | n | n | crossproduct Jacobian |
| PHESSIAN | y | n | n | n | Hessian matrix |
| PSTDERR | y | n | n | n | approx. standard errors |
| PCOV | y | n | n | n | covariance matrices |
| PJACOBI | n | n | n | n | Jacobian |
| LIST | n | n | n | n | model program, variables |
| LISTCODE | n | n | n | n | compiled model program |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
