sr1
Use the Symmetric Rank 1 update method to compute quasi-Hessians
Specification
Alias: None
Arguments: None
Description
The Symmetric Rank 1 (SR1) update (specified with the keyword sr1)
will be used to compute quasi-Hessians.
\[B_{k+1} = B_k + \frac{(y_k - B_k s_k)(y_k - B_k s_k)^T}{(y_k - B_k s_k)^T s_k}\]
where \(B_k\) is the \(k^{th}\) approximation to the Hessian, \(s_k = x_{k+1} - x_k\) is the step and \(y_k = \nabla f_{k+1} - \nabla f_k\) is the corresponding yield in the gradients.
Notes
Initial scaling of \(\frac{y_k^T y_k}{y_k^T s_k} I\) is used for \(B_0\) prior to the first update.
Numerical safeguarding is used to protect against numerically small denominators within the updates.
This safeguarding skips the update if \(|(y_k - B_k s_k)^T s_k| < 10^{-6} ||s_k||_2 ||y_k - B_k s_k||_2\)
