A primal-dual homotopy algorithm for \(\ell _{1}\)-minimization with \(\ell _{\infty }\)-constraints

DOI10.1007/s10589-018-9983-4zbMath1391.90404arXiv1610.10022OpenAlexW2542269046MaRDI QIDQ1639715

Christoph Brauer, Dirk A. Lorenz, Andreas M. Tillmann

Publication date: 13 June 2018

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.10022

zbMATH Keywords

nonsmooth optimizationconvex optimizationhomotopy methodsDantzig selectorprimal-dual methods

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Linear programming (90C05)

Related Items (4)

Inertial proximal ADMM for separable multi-block convex optimizations and compressive affine phase retrieval ⋮ A simple homotopy proximal mapping algorithm for compressive sensing ⋮ Complexity and applications of the homotopy principle for uniformly constrained sparse minimization ⋮ A discrete dynamics approach to sparse calculation and applied in ontology science

Uses Software

• PDCO
• LPbook

Cites Work

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• A mathematical introduction to compressive sensing
• Über diskrete und lineare Tschebyscheff-Approximationen
• A new simple homotopy algorithm for linear programming. I
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• A Constrainedℓ₁Minimization Approach to Sparse Precision Matrix Estimation
• On L1 and Chebyshev estimation
• A Direct Estimation Approach to Sparse Linear Discriminant Analysis
• Decoding by Linear Programming
• DASSO: Connections Between the Dantzig Selector and Lasso
• The Homotopy Principle and Algorithms for Linear Programming
• Atomic Decomposition by Basis Pursuit
• A new approach to variable selection in least squares problems
• Solving Basis Pursuit
• Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine
• Convex Analysis
• Compressed sensing
• Linear programming. Foundations and extensions

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