Adaptive cubic regularization (ARC) and trust-region (TR) methods use modified linear systems to compute their steps. The modified systems consist in adding some multiple of the identity matrix (or a well-chosen positive definite matrix) to the Hessian to obtain a sufficiently positive definite linear system, the so called shifted system. This type of system was first proposed by Levenberg and Marquardt. Some trial and error is often involved to obtain a specified value for this shift parameter. We provide an efficient unified implementation to track the shift parameter; our implementation encompasses many ARC and TR variants.

中文翻译：

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无约束优化的信任域类型算法的统一有效实现

自适应三次正则化（ARC）和信任区域（TR）方法使用修改后的线性系统来计算其步长。修改后的系统包括在Hessian中添加一定数量的单位矩阵（或选择好的正定矩阵），以获得足够正的定线性系统，即所谓的平移系统。这种类型的系统最早是由Levenberg和Marquardt提出的。为了获得该移位参数的指定值，通常需要反复试验。我们提供了一个有效的统一实现来跟踪shift参数；我们的实现包含许多ARC和TR变体。