Is it possible to apply adaptions of the conjugate gradient algorithm i.e. Fletcher-Reeves, Polak-Ribere or others to systems of nonlinear equations? How should the equation system be adjusted so one can use those algorithms?
I am asking this because in all of the literature, the pseudocode says to compute the conjugated directions by gradients, i.e.:
$p_{k+1} = -\nabla f_{k+1} + \beta_{k+1} p_k $ with $\beta_{k+1} = \frac{\nabla f_{k+1}^T \nabla f_{k+1}}{\nabla f_{k}^T \nabla f_{k}}$
But in an system of equations, $\nabla f$ results in the Jacobian. What do I miss?
