AN LDLT TRUST-REGION QUASI-NEWTON METHOD

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 LDLT factorization, scales quadratically with the size of the problem, and is competitive with a conventional line-search method. © 2024 SIAM.