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A note on the complexity of ${L}_{p}$ minimization. (English) Zbl 1226.90076
Summary: We discuss the ${L}_{p}\left(0\le p<1\right)$ minimization problem arising from sparse solution construction and compressed sensing. For any fixed $0, 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.
##### MSC:
 90C26 Nonconvex programming, global optimization 90C51 Interior-point methods
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