1Blurb::
2Use the Symmetric Rank 1 update method to compute quasi-Hessians
3Description::
4The Symmetric Rank 1 (SR1) update (specified with the keyword \c sr1)
5will be used to compute quasi-Hessians.
6
7\f[
8B_{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}
9\f]
10
11where \f$B_k\f$ is the \f$k^{th}\f$ approximation to the Hessian,
12\f$s_k = x_{k+1} - x_k\f$ is the step and
13\f$y_k = \nabla f_{k+1} - \nabla f_k\f$ is the corresponding yield
14in the gradients.
15
16<b> Notes </b>
17
18\li Initial scaling of
19\f$\frac{y_k^T y_k}{y_k^T s_k} I\f$ is used for \f$B_0\f$ prior to the first
20update.
21\li Numerical safeguarding is used
22to protect against numerically small denominators within the updates.
23\li This safeguarding skips the update if
24\f$|(y_k - B_k s_k)^T s_k| < 10^{-6} ||s_k||_2 ||y_k - B_k s_k||_2\f$
25
26Topics::
27Examples::
28Theory::
29Faq::
30See_Also::
31