Time-Data Tradeoffs in Structured Signals Recovery via the Proximal-Gradient Homotopy Method

Xiao Lv; Wei Cui; Yulong Liu

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arXiv · 2104.02861

Time-Data Tradeoffs in Structured Signals Recovery via the Proximal-Gradient Homotopy Method

Xiao Lv·Wei Cui·Yulong Liu

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Abstract

In this paper, we characterize data-time tradeoffs of the proximal-gradient homotopy method used for solving linear inverse problems under sub-Gaussian measurements. Our results are sharp up to an absolute constant factor. We demonstrate that, in the absence of the strong convexity assumption, the proximal-gradient homotopy update can achieve a linear rate of convergence when the number of measurements is sufficiently large. Numerical simulations are provided to verify our theoretical results.

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Xiao Lv, Wei Cui, Yulong Liu. 2021-04-07. Time-Data Tradeoffs in Structured Signals Recovery via the Proximal-Gradient Homotopy Method. https://arxiv.org/abs/2104.02861

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