  For quasi-Newton methods in unconstrained minimization, it is valuable to
develop methods that are robust, i.e., methods that converge on a large number
of problems. Trust-region algorithms are often regarded to be more robust than
line-search methods, however, because trust-region methods are computationally
more expensive, the most popular quasi-Newton implementations use line-search
methods. To fill this gap, we develop a trust-region method that updates an
$LDL^T$ factorization, scales quadratically with the size of the problem, and
is competitive with a conventional line-search method.

Optimization and Control;Numerical Analysis;Numerical Analysis;Computation