The NLP Procedure |
Almost all line-search algorithms use iterative extrapolation
techniques which can easily lead them to (feasible) points
where the objective function is no longer defined.
(e.g., resulting in indefinite matrices for ML estimation)
or difficult to compute (e.g., resulting in floating point
overflows). Therefore, PROC NLP provides options
restricting the step length
or trust region radius
, especially during the first main iterations.
The inner product of the gradient
and the search
direction
is the slope of
along the search direction
. The default starting value
in each line-search
algorithm
during
the main iteration
is computed in three steps:
This value of can be too large and lead
to a difficult or impossible function evaluation, especially
for highly nonlinear functions such as the EXP function.
The INSTEP= option lets you specify
a smaller or larger radius
of the
trust region used in the first iteration of the trust region, double
dogleg, and Levenberg-Marquardt algorithms. The default
initial trust region radius
is the length of the
scaled gradient (Moré 1978). This step corresponds to the
default radius factor of
. In most practical applications of
the TRUREG, DBLDOG, and LEVMAR algorithms, this choice is
successful. However, for
bad initial values and highly nonlinear objective functions
(such as the EXP function), the default start radius can result
in arithmetic overflows. If this happens, you may try decreasing
values of INSTEP=
,
, until the iteration starts
successfully. A small factor
also affects the trust region
radius
of the next steps because the radius is
changed in each iteration by a factor
, depending
on the ratio
expressing the goodness of quadratic function
approximation.
Reducing the radius
corresponds to increasing the ridge
parameter
, producing smaller steps directed more closely
toward the (negative) gradient direction.
Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.