# NP-hardness of $\ell$0 minimization problems: revision and extension to the non-negative setting

Abstract : Sparse approximation arises in many applications and often leads to a constrained or penalized l0 minimization problem, which was proved to be NP-hard. This paper proposes a revision of existing analyses of NP-hardness of the penalized l0 problem and it introduces a new proof adapted from Natarajan's construction (1995). Moreover, we prove that l0 minimization problems with non-negativity constraints are also NP-hard.
Document type :
Conference papers

https://hal.archives-ouvertes.fr/hal-02112180
Contributor : Charles Soussen <>
Submitted on : Friday, April 26, 2019 - 2:56:10 PM
Last modification on : Thursday, May 16, 2019 - 1:30:24 AM

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Nguyen19_revised.pdf
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• HAL Id : hal-02112180, version 1

### Citation

Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. NP-hardness of $\ell$0 minimization problems: revision and extension to the non-negative setting. 13th International Conference on Sampling Theory and Applications, SampTA 2019, Jul 2019, Bordeaux, France. ⟨hal-02112180⟩

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