Nonlinear Optimization Examples |
Printing the Optimization History
Each optimization and least-squares subroutine prints
the optimization history, as long as opt
and you do not specify the "ptit" module argument.
You can use this output to check for possible convergence problems.
If you specify the "ptit" argument, you can enter a print
command inside the module, which is called at each iteration.
The amount of information printed
depends on the opt[2] argument.
See the section "Options Vector".
The output consists of three main parts:
- Optimization Start Output
The following information about the initial
state of the optimization can be printed:
- 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, at least
one of which is temporarily released from the
working set due to negative Lagrange multipliers.
- the value of the objective
function at the starting point
- the value of the largest absolute
(projected) gradient element
- the initial trust-region radius for
the NLPTR and NLPLM subroutines
- General Iteration History
In general, the iteration history consists of one
line of printed output for each iteration, with
the exception of the Nelder-Mead simplex method.
The NLPNMS subroutine prints a line only after several
internal iterations because some of the termination tests
are time-consuming compared to the simplex operations and
because the subroutine typically uses many iterations.
The iteration history always includes the following columns:
- iter is the iteration number.
- nrest is the number of iteration restarts.
- nfun is the number of function calls.
- act is the number of active constraints.
- optcrit is the value of the
optimization criterion.
- difcrit is the difference
between adjacent function values.
- maxgrad is the maximum of the
absolute (projected) gradient components.
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.
Some subroutines print additional information at each
iteration; for details see the entry corresponding to
each subroutine in the "Nonlinear Optimization and Related Subroutines" section.
- Optimization Result Output
The output ends with the following
information about 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 (+),
there are more active constraints, at least one
of which is temporarily released from the
working set due to negative Lagrange multipliers.
- the value of the objective function at the final point
- the value of the largest absolute
(projected) gradient element
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.