The rows and columns of the Hessian matrix can be scaled when you use the trust region, Newton-Raphson, and double-dogleg optimization techniques. Each element
,
is divided by the scaling factor
, where the scaling vector
is iteratively updated in a way specified by the HESCAL=
option, as follows:
![](images/statug_nlmixed0296.png)
No scaling is done (equivalent to
).
![](images/statug_nlmixed0298.png)
First iteration and each restart iteration sets:
![](images/statug_nlmixed0299.png)
Refer to Moré (1978):
![](images/statug_nlmixed0300.png)
Refer to Dennis, Gay, and Welsch (1981):
![](images/statug_nlmixed0302.png)
is reset in each iteration:
In the preceding equations,
is the relative machine precision or, equivalently, the largest double-precision value that, when added to 1, results in 1.
Copyright © SAS Institute, Inc. All Rights Reserved.