Compact representations of structured BFGS matrices

• Tác giả: Johannes J Brust, Di, Sven Leyffer, Cosmin G Petra, Zichao
• Ngôn ngữ: eng
• Ký hiệu phân loại: 512.897 Algebra
• Thông tin xuất bản: 2022
• Bộ sưu tập: Metadata
• ID: 195587

Tóm tắt

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.