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A note on the complexity of L p minimization. (English) Zbl 1226.90076
Summary: We discuss the L p (0p<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.
MSC:
90C26Nonconvex programming, global optimization
90C51Interior-point methods
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