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First-order optimality condition of basis pursuit denoise problem

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Abstract

A new first-order optimality condition for the basis pursuit denoise (BPDN) problem is derived. This condition provides a new approach to choose the penalty parameters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan Province, P. R. China

    Wei Zhu  (朱 玮) & Shi Shu  (舒 适)

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, Hunan Province, P. R. China

    Shi Shu  (舒 适)

  3. Department of Mathematics and Computational Science, College of Science, National University of Defense Technology, Changsha, 410073, P. R. China

    Li-zhi Cheng  (成礼智)

Authors
  1. Wei Zhu  (朱 玮)
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  2. Shi Shu  (舒 适)
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  3. Li-zhi Cheng  (成礼智)
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Corresponding author

Correspondence to Li-zhi Cheng  (成礼智).

Additional information

Project supported by the National Natural Science Foundation of China (No. 61271014), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20124301110003), and the Graduated Students Innovation Fund of Hunan Province (No.CX2012B238)

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Zhu, W., Shu, S. & Cheng, Lz. First-order optimality condition of basis pursuit denoise problem. Appl. Math. Mech.-Engl. Ed. 35, 1345–1352 (2014). https://doi.org/10.1007/s10483-014-1860-9

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  • DOI: https://doi.org/10.1007/s10483-014-1860-9

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2010 Mathematics Subject Classification

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