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A note on the complexity ofLp minimization

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Abstract

We discuss theLp (0 ≤p < 1) minimization problem arising from sparse solution construction and compressed sensing. For any fixed 0 < p < 1, we prove that finding the global minimal value of the problem is strongly NP-Hard, but computing a local minimizer of the problem can be done in polynomial time. We also develop an interior-point potential reduction algorithm with a provable complexity bound and demonstrate preliminary computational results of effectiveness of the algorithm.

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Authors and Affiliations

  1. Antai School of Economics and Management, Shanghai Jiao Tong University, Shanghai, 200052, China

    Dongdong Ge

  2. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA

    Xiaoye Jiang

  3. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA

    Yinyu Ye

Authors
  1. Dongdong Ge

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  2. Xiaoye Jiang

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  3. Yinyu Ye

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Correspondence toDongdong Ge.

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Ge, D., Jiang, X. & Ye, Y. A note on the complexity ofLp minimization.Math. Program.129, 285–299 (2011). https://doi.org/10.1007/s10107-011-0470-2

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