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 , is divided by the scaling factor , where the scaling vector is iteratively updated in a way specified by the HESCAL= option, as follows:

No scaling is done (equivalent to ).

First iteration and each restart iteration sets:


Refer to Moré (1978):


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


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.