论文标题
Hessians计算的新框架
A new framework for the computation of Hessians
论文作者
论文摘要
我们使用图形模型和代数模型通过自动分化来研究Hessian矩阵的计算。该图模型揭示了计算Hessian所涉及的固有对称性。基于Griewank和Walther的状态转换的代数模型将Hessian作为公式的计算综合。这些双重观点（图形和代数）为Hessian计算带来了新的框架。通过开发Edge_pushing（一种全新的反向Hessian计算算法）可以完全利用Hessian的对称性来说明这一点。计算实验比较了来自可爱收藏的16个功能的Edge_pushing的性能与作为软件Adol-C驱动程序可用的两种算法可用的算法，结果非常有前途。
We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on Griewank and Walther's state transformations, synthesizes the calculation of the Hessian as a formula. These dual points of view, graphical and algebraic, lead to a new framework for Hessian computation. This is illustrated by developing edge_pushing, a new truly reverse Hessian computation algorithm that fully exploits the Hessian's symmetry. Computational experiments compare the performance of edge_pushing on sixteen functions from the CUTE collection against two algorithms available as drivers of the software ADOL-C, and the results are very promising.
