Nonmonotone Barzilai-Borwein gradient algorithm for \(\ell_1\)-regularized nonsmooth minimization in compressive sensing
type: Item
instance of: scholarly article
title: Nonmonotone Barzilai-Borwein gradient algorithm for \(\ell_1\)-regularized nonsmooth minimization in compressive sensing
zbMATH Open document ID: 1306.65216
author: Soon-Yi Wu
author: Liqun Qi
author: Yunhai Xiao
published in: Journal of Scientific Computing
publication date: 2014-11-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.4538
review text: The authors propose, analyze and test a new practical algorithm to solve the separable nonsmooth minimization problem consisting of an \(\ell_1\)-norm regularized term and a continuously differentiable term. This type of problem mainly appears in signal/image processing, compressive sensing, machine learning, and linear inverse problem. However, the problem is challenging because of the non-smoothness of the regularization term. For various practical problems, either the computing efforts of the Hessian matrices are very expensive or the evaluation of the Hessian is difficult, the Hessian is not even available analytically. These challenges lead to the quasi-Newton method, which generates a series of Hessian approximation through the use of the gradient while maintaining a fast rate of convergence.
reviewed by: Jan Lovíšek
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6373685
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: nonconvex optimization
zbMATH Keywords: Barzilai-Borwein gradient algorithm
zbMATH Keywords: nonmonotone line search
zbMATH Keywords: \(\ell_1\) regularization
zbMATH Keywords: compressive sensing
zbMATH Keywords: gradient algorithm
zbMATH Keywords: iteration
zbMATH Keywords: numerical experiments
zbMATH Keywords: smooth term
zbMATH Keywords: globally convergent
zbMATH Keywords: quasi-Newton method
zbMATH Keywords: Hessian approximation
zbMATH Keywords: positive components
describes a project that uses: FPC_AS
describes a project that uses: SPGL1
describes a project that uses: NESTA
describes a project that uses: L-BFGS
describes a project that uses: CUTEr
describes a project that uses: TwIST
MaRDI profile type: Publication
OpenAlex ID: W2067425611
arXiv ID: 1207.4538
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Nonmonotone Barzilai-Borwein gradient algorithm for \(\ell_1\)-regularized nonsmooth minimization in compressive sensing (cites work)
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Nonmonotone Barzilai-Borwein gradient algorithm for \(\ell_1\)-regularized nonsmooth minimization in compressive sensing (DOI)
DOI: 10.1007/S10915-013-9815-8