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2.5.1 Newton Methods Overview     continued...

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.