Compact representations of structured BFGS matrices

Johannes J. Brust, Zichao, Di, Sven Leyffer and Cosmin G. Petra
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Johannes J. Brust: Wendy
Zichao: Wendy

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Abstract: 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.

Date: 2022-07
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Published in Computational Optimization and Applications 80:55-88 (2021)

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