A note on the complexity of \(L _{p }\) minimization. (English) Zbl 1226.90076

Summary: We discuss the \(L _{p } (0 \leq p < 1)\) 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.


90C26 Nonconvex programming, global optimization
90C51 Interior-point methods
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