H. Attouch, J. Bolte, and B. Svaiter, Convergence of descent methods for semialgebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods, Mathematical Programming, pp.91-129, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00790042

A. Boisbunon, Model selection: a decision-theoretic approach. Thesis, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00793898

S. Bourguignon, J. Ninin, H. Carfantan, and M. Mongeau, Exact Sparse Approximation Problems via Mixed-Integer Programming: Formulations and Computational Performance, IEEE Transactions on Signal Processing, vol.64, issue.6, 2015.
DOI : 10.1109/TSP.2015.2496367

URL : https://hal.archives-ouvertes.fr/hal-01254856

L. Breiman, Better Subset Regression Using the Nonnegative Garrote, Technometrics, vol.37, issue.4, pp.373-384, 1995.
DOI : 10.1080/01621459.1980.10477428

J. Emmanuel, J. Candès, T. Romberg, and . Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, vol.52, issue.2, pp.489-509, 2006.

J. Emmanuel, . Candes, B. Michael, . Wakin, P. Stephen et al., Enhancing sparsity by reweighted 1 minimization, Journal of Fourier analysis and applications, vol.14, pp.5-6877, 2008.

E. Chouzenoux, A. Jezierska, J. Pesquet, and H. Talbot, A Majorize-Minimize Subspace Approach for $\ell_2-\ell_0$ Image Regularization, SIAM Journal on Imaging Sciences, vol.6, issue.1, pp.563-591, 2013.
DOI : 10.1137/11085997X

H. Frank and . Clarke, Optimization and nonsmooth analysis, SIAM, vol.5, 1990.

H. Dong, K. Chen, and J. Linderoth, Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection. Optimization Online, 2015.

L. David and . Donoho, For most large underdetermined systems of linear equations the minimal 1 norm solution is also the sparsest solution, Communications on Pure and Applied Mathematics, vol.59, issue.6, pp.797-829, 2006.

J. Fan and R. Li, Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties, Journal of the American Statistical Association, vol.96, issue.456, pp.1348-1360, 2001.
DOI : 10.1198/016214501753382273

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.4174

S. Foucart and M. Lai, Sparsest solutions of underdetermined linear systems via <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>???</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:math>-minimization for <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>q</mml:mi><mml:mo>???</mml:mo><mml:mn>1</mml:mn></mml:math>, Applied and Computational Harmonic Analysis, vol.26, issue.3, pp.395-407, 2009.
DOI : 10.1016/j.acha.2008.09.001

G. Fung and O. Mangasarian, Equivalence of Minimal ??? 0- and ??? p -Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p, Journal of Optimization Theory and Applications, vol.22, issue.1, pp.1-10, 2011.
DOI : 10.1137/1.9781611971255

G. Gasso, A. Rakotomamonjy, and S. Canu, Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming, IEEE Transactions on Signal Processing, vol.57, issue.12, pp.4686-4698, 2009.
DOI : 10.1109/TSP.2009.2026004

URL : https://hal.archives-ouvertes.fr/hal-00439453

P. Gong, C. Zhang, Z. Lu, J. Huang, and J. Ye, A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems, Proceedings of The 30th International Conference on Machine Learning, pp.37-45, 2013.

L. Hoai-an, . Thi, H. M. Pham-dinh, X. T. Le, and . Vo, DC approximation approaches for sparse optimization, European Journal of Operational Research, vol.244, issue.1, pp.26-46, 2015.

L. Hoai-an, H. M. Thi, T. Le, and . Pham-dinh, Feature selection in machine learning: an exact penalty approach using a difference of convex function algorithm, Machine Learning, pp.1-24, 2014.

G. Stéphane, Z. Mallat, and . Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.

. Balas-kausik-natarajan, Sparse Approximate Solutions to Linear Systems, SIAM Journal on Computing, vol.24, issue.2, pp.227-234, 1995.
DOI : 10.1137/S0097539792240406

M. Nikolova, Description of the Minimizers of Least Squares Regularized with $\ell_0$-norm. Uniqueness of the Global Minimizer, SIAM Journal on Imaging Sciences, vol.6, issue.2, pp.904-937, 2013.
DOI : 10.1137/11085476X

M. Nikolova, Relationship between the optimal solutions of least squares regularized with ??? 0 -norm and constrained by k-sparsity, Applied and Computational Harmonic Analysis, vol.41, issue.1, pp.237-265, 2016.
DOI : 10.1016/j.acha.2015.10.010

URL : https://hal.archives-ouvertes.fr/hal-00944006

P. Ochs, A. Dosovitskiy, T. Brox, and T. Pock, On Iteratively Reweighted Algorithms for Nonsmooth Nonconvex Optimization in Computer Vision, SIAM Journal on Imaging Sciences, vol.8, issue.1, pp.331-372, 2015.
DOI : 10.1137/140971518

Y. Chandra-pati, R. Rezaiifar, and P. Krishnaprasad, Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition, Signals, Systems and Computers Conference Record of The Twenty-Seventh Asilomar Conference on, pp.40-44, 1993.

A. Repetti, M. Q. Pham, L. Duval, E. Chouzenoux, and J. Pesquet, Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed <formula formulatype="inline"><tex Notation="TeX">${\ell _1}/{\ell _2}$</tex></formula> Regularization, IEEE Signal Processing Letters, vol.22, issue.5, pp.539-543, 2015.
DOI : 10.1109/LSP.2014.2362861

E. Soubies, L. Blanc-féraud, and G. Aubert, A Continuous Exact $\ell_0$ Penalty (CEL0) for Least Squares Regularized Problem, SIAM Journal on Imaging Sciences, vol.8, issue.3, pp.1607-1639, 2015.
DOI : 10.1137/151003714

C. Soussen, J. Idier, D. Brie, and J. Duan, From Bernoulli&#x2013;Gaussian Deconvolution to Sparse Signal Restoration, IEEE Transactions on Signal Processing, vol.59, issue.10, pp.4572-4584, 2011.
DOI : 10.1109/TSP.2011.2160633

C. Soussen, J. Idier, J. Duan, and D. Brie, Homotopy Based Algorithms for <formula formulatype="inline"><tex Notation="TeX">$\ell _{\scriptscriptstyle 0}$</tex></formula>-Regularized Least-Squares, IEEE Transactions on Signal Processing, vol.63, issue.13, pp.3301-3316, 2015.
DOI : 10.1109/TSP.2015.2421476

A. Joel and . Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Transactions on Information Theory, vol.50, issue.10, pp.2231-2242, 2004.

C. Zhang, Discussion: One-step sparse estimates in nonconcave penalized likelihood models. The Annals of Statistics, pp.1553-1560, 2008.

C. Zhang, Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, pp.894-942, 2010.
DOI : 10.1214/09-aos729

URL : http://arxiv.org/abs/1002.4734

N. Zhang and Q. Li, On optimal solutions of the constrained 0 regularization and its penalty problem, Inverse Problems, vol.33, issue.2, p.2017

T. Zhang, Multi-stage convex relaxation for learning with sparse regularization, Advances in Neural Information Processing Systems, pp.1929-1936, 2009.
DOI : 10.3150/12-bej452

URL : http://arxiv.org/abs/1106.0565

H. Zou, The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association, vol.101, issue.476, pp.1418-1429, 2006.
DOI : 10.1198/016214506000000735

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.404