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Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

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Mengqi Hu, Yifei Lou, Bao Wang, Ming Yan, Xiu Yang, Qiang Ye

Optimization and Control · Submitted 25 Aug 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

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arXiv ID2208.12183 (version 2)
Pith ID6PRU4TU2, Pith's permanent record of this paper and its review
CitationBao Wang, Mengqi Hu, Ming Yan, Qiang Ye, Xiu Yang, Yifei Lou. "Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum." arXiv:2208.12183 (2022). https://pith.science/paper/6PRU4TU2
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,293 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.48 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. contribution 0.96 0.86 0.28 asserted 0.99
s1 Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. method 0.56 0.58 0.03 asserted 0.92
s2 In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. method 0.97 0.92 0.06 asserted 1.00
s3 This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. method 0.96 0.84 0.06 asserted 1.00
s4 We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods. result 0.52 0.91 0.52 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.78.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

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