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- W4289019726 abstract "We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a highly efficient evaluation of the proximal mapping. The key to this efficiency is a general proximal calculus in the new metric. By using duality, formulas are derived that relate the proximal mapping in a rank-$r$ modified metric to the original metric. We also describe efficient implementations of the proximity calculation for a large class of functions; the implementations exploit the piece-wise linear nature of the dual problem. Then, we apply these results to acceleration of composite convex minimization problems, which leads to elegant quasi-Newton methods for which we prove convergence. The algorithm is tested on several numerical examples and compared to a comprehensive list of alternatives in the literature. Our quasi-Newton splitting algorithm with the prescribed metric compares favorably against state-of-the-art. The algorithm has extensive applications including signal processing, sparse recovery, machine learning and classification to name a few." @default.
- W4289019726 created "2022-07-31" @default.
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- W4289019726 date "2019-01-01" @default.
- W4289019726 modified "2023-09-23" @default.
- W4289019726 title "ON QUASI-NEWTON FORWARD-BACKWARD SPLITTING: PROXIMAL CALCULUS AND CONVERGENCE" @default.
- W4289019726 hasPublicationYear "2019" @default.
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