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2.5.1 Newton Methods Overview     continued...

All Newton methods are based on approximating the objective function locally by a quadratic model and then minimizing that function approximately. The quadratic model of the objective function f at along is given by the expansion

The minimum of the right-hand side is achieved when is the minimum of the quadratic function:

Alternatively, such a Newton direction satisfies the linear system of n simultaneous equations, known as the Newton equation: