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.

翻译：针对无约束极小化中的拟牛顿方法，开发具有鲁棒性（即在大量问题上均能收敛）的方法具有重要价值。信赖域算法通常被认为比线搜索方法更稳健，但由于信赖域方法计算代价更高，最常用的拟牛顿实现仍采用线搜索方法。为填补这一空白，我们提出一种信赖域方法，该方法更新 $LDL^T$ 分解，其计算复杂度随问题规模呈二次增长，且与传统线搜索方法具有竞争力。