Editing Maximum likelihood estimation (section)

==== [[Broyden–Fletcher–Goldfarb–Shanno algorithm]] ====
BFGS also gives a solution that is symmetric and positive-definite:

<math display="block">B_{k+1} = B_k + \frac{y_k y_k^\mathsf{T}}{y_k^\mathsf{T} s_k} - \frac{B_k s_k s_k^\mathsf{T} B_k^\mathsf{T}}{s_k^\mathsf{T} B_k s_k}\ ,</math>

where

<math display="block">y_k = \nabla\ell(x_k + s_k) - \nabla\ell(x_k),</math>
<math display="block">s_k = x_{k+1} - x_k.</math>

BFGS method is not guaranteed to converge unless the function has a quadratic [[Taylor expansion]] near an optimum. However, BFGS can have acceptable performance even for non-smooth optimization instances