The NLMIXED Procedure

Hessian Scaling

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 $\text{[math]}$ , $\text{[math]}$ is divided by the scaling factor $\text{[math]}$ , where the scaling vector $\text{[math]}$ is iteratively updated in a way specified by the HESCAL= $\text{[math]}$ option, as follows:

$\text{[math]}$

No scaling is done (equivalent to $\text{[math]}$ ).

$\text{[math]}$

First iteration and each restart iteration sets:

$\text{[math]}$

$\text{[math]}$

Refer to Moré (1978):

$\text{[math]}$

$\text{[math]}$

Refer to Dennis, Gay, and Welsch (1981):

$\text{[math]}$

$\text{[math]}$

$\text{[math]}$ is reset in each iteration:

$\text{[math]}$

In the preceding equations, $\text{[math]}$ is the relative machine precision or, equivalently, the largest double-precision value that, when added to 1, results in 1.