Issues with SR1 algorithm

[stefan-k]

The symmetric rank-one (SR1) algorithm fails under certain conditions. In particular, it produces search directions which are not descent directions and therefore not accepted in the line searches. It is unclear to me whether this is a problem of the implementation or a general problem of this method. I was unable to find another implementation to compare to.

The example succeeds for this initial parameter vector:

let init_param: Array1<f64> = array![-1.2, 1.0, -5.0, 2.0, 3.0, 2.0, 4.0, 5.0];

but fails for this initial parameter vector:

let init_param: Array1<f64> = array![-1.2, 1.0, -5.0, 2.0, 3.0, 2.0, 4.0, 5.0];

The implementation includes a rule for skipping the Hessian update for cases where the denominator of the Hessian update is very small, but this rule does not seem to kick in for most if not all cases I've tried.

Any help on this is highly appreciated!