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• W3159485596 abstract "We study the convergence rate of gradient-based local search methods for solving low-rank matrix recovery problems with general objectives in both symmetric and asymmetric cases, under the assumption of the restricted isometry property. First, we develop a new technique to verify the Polyak-Lojasiewicz inequality in a neighborhood of the global minimizers, which leads to a local linear convergence region for the gradient descent method. Second, based on the local convergence result and a sharp strict saddle property proven in this paper, we present two new conditions that guarantee the global linear convergence of the perturbed gradient descent method. The developed local and global convergence results provide much stronger theoretical guarantees than the existing results. As a by-product, this work significantly improves the existing bounds on the RIP constant required to guarantee the non-existence of spurious solutions." @default.
• W3159485596 created "2021-05-10" @default.
• W3159485596 creator A5039984791 @default.
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• W3159485596 date "2022-06-28" @default.
• W3159485596 modified "2023-09-26" @default.
• W3159485596 title "Local and Global Linear Convergence of General Low-Rank Matrix Recovery Problems" @default.
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• W3159485596 doi "https://doi.org/10.1609/aaai.v36i9.21252" @default.
• W3159485596 hasPublicationYear "2022" @default.
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