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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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Antai School of Economics and Management, Shanghai Jiao Tong University, Shanghai, 200052, China
Dongdong Ge
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA
Xiaoye Jiang
Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA
Yinyu Ye
- Dongdong Ge
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- Xiaoye Jiang
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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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