Newton variants are constructed by combining various strategies for the
individual components above. These involve procedures for formulating
or , dealing with structures of
indefinite Hessians,
and solving for the * modified Newton* search direction. For example,
when is approximated by * finite differences*, the discrete Newton
subclass emerges [16]. When , or its
inverse, is approximated by some modification of the previously
constructed matrix (see below), QN methods are formed [16,17].
When
is nonzero, TN methods result
[18,47,55,56,57]
since the solution of the Newton
system is * truncated* before completion.