An alternating direction method for finding Dantzig selectors

DOI10.1016/j.csda.2012.04.019zbMath1255.62096arXiv1011.4604OpenAlexW2143655919WikidataQ57511229 ScholiaQ57511229MaRDI QIDQ1927184

Zhaosong Lu, Ting Kei Pong, Yong Zhang

Publication date: 30 December 2012

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.4604

zbMATH Keywords

gradient methodnonomonotone line search

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Applications of mathematical programming (90C90)

Related Items

Further properties of the forward-backward envelope with applications to difference-of-convex programming, An alternating direction method of multipliers for MCP-penalized regression with high-dimensional data, The regularization continuation method with an adaptive time step control for linearly constrained optimization problems, Finding Dantzig selectors with a proximity operator based fixed-point algorithm, A primal Douglas-Rachford splitting method for the constrained minimization problem in compressive sensing, A fast splitting method tailored for Dantzig selector, The matrix splitting based proximal fixed-point algorithms for quadratically constrained \(\ell_{1}\) minimization and Dantzig selector, Peaceman-Rachford splitting for a class of nonconvex optimization problems, The regularization continuation method for optimization problems with nonlinear equality constraints, Statistical multiresolution Dantzig estimation in imaging: fundamental concepts and algorithmic framework, A partially proximal linearized alternating minimization method for finding Dantzig selectors, Comparison of several fast algorithms for projection onto an ellipsoid, An ADMM with continuation algorithm for non-convex SICA-penalized regression in high dimensions, The Dantzig selector: recovery of signal via ℓ ₁ − αℓ ₂ minimization, Efficient Sparse Hessian-Based Semismooth Newton Algorithms for Dantzig Selector

Uses Software

• RecPF
• L1-MAGIC
• TFOCS
• BMSS

Cites Work

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• Approximation accuracy, gradient methods, and error bound for structured convex optimization
• Primal-dual first-order methods with \({\mathcal {O}(1/\varepsilon)}\) iteration-complexity for cone programming
• An augmented Lagrangian approach for sparse principal component analysis
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Templates for convex cone problems with applications to sparse signal recovery
• Alternating direction method for covariance selection models
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
• Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
• Variable selection and dependency networks for genomewide data
• DASSO: Connections Between the Dantzig Selector and Lasso
• Regularization and Variable Selection Via the Elastic Net
• An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
• Interior Gradient and Proximal Methods for Convex and Conic Optimization