A Unified View of Exact Continuous Penalties for $\ell_2$-$\ell_0$ Minimization
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Publication:5359501
DOI10.1137/16M1059333zbMath1375.65086MaRDI QIDQ5359501
Laure Blanc-Féraud, Emmanuel Soubies, Gilles Aubert
Publication date: 25 September 2017
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
global minimizerslocal minimizerssparse modelingminimizers equivalence\(\ell_0\)-regularized least squaresexact \(\ell_0\) penaltiesexact reformulationunderdeterminated linear system
Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26)
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Cites Work
- Unnamed Item
- Nearly unbiased variable selection under minimax concave penalty
- The Adaptive Lasso and Its Oracle Properties
- Relationship between the optimal solutions of least squares regularized with \(\ell_{0}\)-norm and constrained by \(k\)-sparsity
- DC approximation approaches for sparse optimization
- Equivalence of minimal \(\ell _{0}\)- and \(\ell _{p }\)-norm solutions of linear equalities, inequalities and linear programs for sufficiently small \(p\)
- Enhancing sparsity by reweighted \(\ell _{1}\) minimization
- Feature selection in machine learning: an exact penalty approach using a difference of convex function algorithm
- Sparsest solutions of underdetermined linear systems via \( \ell _q\)-minimization for \(0<q\leqslant 1\)
- Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
- Sparse learning via Boolean relaxations
- A Majorize-Minimize Subspace Approach for $\ell_2-\ell_0$ Image Regularization
- Description of the Minimizers of Least Squares Regularized with $\ell_0$-norm. Uniqueness of the Global Minimizer
- On optimal solutions of the constrained ℓ 0 regularization and its penalty problem
- Better Subset Regression Using the Nonnegative Garrote
- A Continuous Exact $\ell_0$ Penalty (CEL0) for Least Squares Regularized Problem
- Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Greed is Good: Algorithmic Results for Sparse Approximation
- Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
- Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming
- From Bernoulli–Gaussian Deconvolution to Sparse Signal Restoration
- Homotopy Based Algorithms for $\ell _{\scriptscriptstyle 0}$-Regularized Least-Squares
- Exact Sparse Approximation Problems via Mixed-Integer Programming: Formulations and Computational Performance
- Sparse Approximate Solutions to Linear Systems
- Matching pursuits with time-frequency dictionaries
- On Iteratively Reweighted Algorithms for Nonsmooth Nonconvex Optimization in Computer Vision
- For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution
- Discussion: One-step sparse estimates in nonconcave penalized likelihood models
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