Nonlinear conjugate gradient method

In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2 , {\displaystyle \displaystyle f(x)=\|Ax-b\|^{2},} the minimum of f {\displaystyle f} is obtained when the gradient is 0: ∇ x f = 2 A T ( A x − b ) = 0 {\displaystyle \nabla _{x}f=2A^{T}(Ax-b)=0} .

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