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 Hi,j, i,j = 1, ... ,n is divided by the
scaling factor di dj, where the scaling vector
d = (d1, ... ,dn) is iteratively updated in a way
specified by the HESCAL=i option, as follows.
In the preceding equations, is the relative machine
precision or, equivalently, the largest double precision value that,
when added to 1, results in 1.
- i = 0:
- No scaling is done (equivalent to di=1).
- First iteration and each restart iteration sets:
- i = 1:
- Refer to Mor (1978):
- i = 2:
- Refer to Dennis, Gay, and Welsch (1981):
- i = 3:
- di is reset in each iteration:
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