论文标题
结构化BFGS矩阵的紧凑表示
Compact representations of structured BFGS matrices
论文作者
论文摘要
对于一般的大规模优化问题，存在紧凑的表示，其中递归准牛顿更新公式表示为紧凑的矩阵因子化。对于目标函数包含其他结构的问题，所谓的结构化准牛顿方法可利用可用的第二个衍生信息和近似不可用的第二个衍生物。本文开发了两个结构化Broyden-Fletcher-Goldfarb-Shanno更新公式的紧凑表示。紧凑的表示可以有效地记忆和初始化策略。描述和测试了两种有限的存储线搜索算法，包括现实世界中的大规模成像应用程序。
For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described and tested on a collection of problems, including a real world large scale imaging application.
