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