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I have noticed that some geophysicists
have adopted a risky method of nonlinear optimization,
which is not advocated in the professional optimization literature.
This risky method is to linearize a goal
(with a multiparameter model space),
then optimize the linearized goal,
then relinearize, etc.
The safer method is to relinearize after each step of CD.
An instructive example
I learned about many years ago was earthquake epicenter location.
Model space is latitude, longitude, and origin time.
When people added a new variable, the depth,
the solutions went wild
until they learned to restrict the depth to zero
until the other three parameters were stabilized.
Apparently the instability stems from the fact
that depth and origin time affect distant receivers in a similar way.