算法XXX：SC-SR1：用于求解形状变化L-SR1置信域子问题的Matlab软件
Algorithm XXX: SC-SR1: Matlab software for solving shape-changing L-SR1 trust-region subproblems
摘要：
我们提出了一个MATLAB实现的对称秩一（SC-SR 1）方法，解决置信域。子问题时，有限内存对称秩一（L-SR 1）矩阵代替真正的黑塞矩阵，可用于大规模优化。该方法利用两个形状变化范数[Burdakov and Yuan 2002; Burdakov et al. 2017]将置信域子问题分解为两个单独的问题。使用所提出的规范之一，由此产生的子问题有封闭形式的解决方案。同时，使用其他提出的规范，所产生的子问题之一有一个封闭的形式的解决方案，而另一个是很容易解决的使用技术，利用L-SR 1矩阵的结构。数值结果表明，SC-SR 1方法能够解决置信域子问题，以高精度，即使在所谓的“硬情况”。当集成到一个置信域算法，大量的数值实验表明，所提出的算法表现良好，当与广泛使用的求解器，如截断CG。
英文摘要：
We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region. subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix, which can be used for large-scale optimization. The method takes advantage of two shape-changing norms[Burdakov and Yuan 2002; Burdakov et al. 2017] to decompose the trust-region subproblem into two separate problems. Using one of the proposed norms, the resulting subproblems have closed-form solutions. Meanwhile, using the other proposed norm, one of the resulting subproblems has a closed-form solution while the other is easily solvable using techniques that exploit the structure of L-SR1 matrices. Numerical results suggest that the SC-SR1 method is able to solve trust-region subproblems to high accuracy even in the so-called "hard case". When integrated into a trust-region algorithm, extensive numerical experiments suggest that the proposed algorithms perform well, when compared with widely used solvers, such as truncated CG.
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