Convergence rates of accelerated proximal gradient algorithms under independent noise

Sun, Tao; Barrio, Roberto; Jiang, Hao; Cheng, Lizhi

doi:10.1007/s11075-018-0565-4

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…Direct use of forward-backward splitting method to (11) yields the following scheme Xk+1=scriptSγλ(Xk−γ(Q∘Xk−Q∘B+μXk)), where γ is the stepsize. It has been well-known that the forward-backward splitting can be accelerated by the Nesterov technique which is frequently used in sparse or low-rank signal processing [26,27,28,29,30,31,32]. By introducing an auxiliary positive sequence (tk)k≥0 with t0=1 and (Yk)k≥0, the accelerated scheme can be described as: for any given X0, set Y0=X0, t0=1,…”

Section: Problem Formulation and The Solutionmentioning

confidence: 99%

Low-Energy Data Collection in Wireless Sensor Networks Based on Matrix Completion

Sun

Geng

et al. 2019

Sensors

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Sparse sensing schemes based on matrix completion for data collection have been proposed to reduce the power consumption of data-sensing and transmission in wireless sensor networks (WSNs). While extensive efforts have been made to improve the recovery accuracy from the sparse samples, it is usually at the cost of running time. Moreover, most data-collection methods are difficult to implement with low sampling ratio because of the communication limit. In this paper, we design a novel data-collection method including a Rotating Random Sparse Sampling method and a Fast Singular Value Thresholding algorithm. With the proposed method, nodes are in the sleep mode most of the time, and the sampling ratio varies over time slots during the sampling process. From the samples, a corresponding algorithm with Nesterov technique is given to recover the original data accurately and fast. With two real-world data sets in WSNs, simulations verify that our scheme outperforms other schemes in terms of energy consumption, reconstruction accuracy, and rate. Moreover, the proposed sampling method enhances the recovery algorithm and prolongs the lifetime of WSNs.

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Section: Problem Formulation and The Solutionmentioning

confidence: 99%

Low-Energy Data Collection in Wireless Sensor Networks Based on Matrix Completion

Sun

Geng

et al. 2019

Sensors

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“…where h is the stepsize, prox is the proximal operator and e k is the noise. In the convex case, this algorithm is discussed in [38,29], and the acceleration is studied in [31].…”

Section: Inexact Nonconvex Proximal Gradient Algorithmmentioning

confidence: 99%

A convergence framework for inexact nonconvex and nonsmooth algorithms and its applications to several iterations

Sun¹,

Jiang²,

Cheng³

et al. 2017

Preprint

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In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm, which cannot be included in previous framework. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under an assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed semi-algebraic property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to several classical inexact nonconvex iterative algorithms and derive the corresponding convergence results.

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The lidar denoising algorithm based on an improved correlation parameter of ensemble empirical mode decomposition

Tan,

Zhang,

Sun

et al. 2024

J. Korean Phys. Soc.

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Convergence rates of accelerated proximal gradient algorithms under independent noise

Cited by 6 publications

References 32 publications

Low-Energy Data Collection in Wireless Sensor Networks Based on Matrix Completion

Low-Energy Data Collection in Wireless Sensor Networks Based on Matrix Completion

A convergence framework for inexact nonconvex and nonsmooth algorithms and its applications to several iterations

The lidar denoising algorithm based on an improved correlation parameter of ensemble empirical mode decomposition

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