Proximal Mapping for Symmetric Penalty and Sparsity

DOI10.1137/17M1116544zbMath1390.90438OpenAlexW2788039246MaRDI QIDQ4606656

Nadav Hallak, Amir Beck

Publication date: 9 March 2018

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1116544

zbMATH Keywords

optimality conditionsproximal gradientsymmetric setsnonconvex proximal operatorsparse regularizer

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

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Uses Software

• PDCO
• GESPAR

Cites Work

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• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• The sparse principal component analysis problem: optimality conditions and algorithms
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Iterative thresholding for sparse approximations
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions, and Algorithms
• Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms
• Description of the Minimizers of Least Squares Regularized with $\ell_0$-norm. Uniqueness of the Global Minimizer
• Introduction to Nonlinear Optimization
• Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems
• Decoding by Linear Programming
• Just relax: convex programming methods for identifying sparse signals in noise
• Sparse and Redundant Representations
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• Atomic Decomposition by Basis Pursuit
• Structured Compressed Sensing: From Theory to Applications
• GESPAR: Efficient Phase Retrieval of Sparse Signals
• Sparse Approximate Solutions to Linear Systems
• Convex Analysis on the Hermitian Matrices
• Reweighted $\ell_1$-Minimization for Sparse Solutions to Underdetermined Linear Systems
• Sparse Approximation via Penalty Decomposition Methods
• Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ ¹ minimization
• Compressed sensing