A hybrid quasi-Newton projected-gradient method with application to Lasso and basis-pursuit denoising

  • We propose a new algorithm for the optimization of convex functions over a polyhedral set in Rn. The algorithm extends the spectral projected-gradient method with limited-memory BFGS iterates restricted to the present face whenever possible. We prove convergence of the algorithm under suitable conditions and apply the algorithm to solve the Lasso problem, and consequently, the basis-pursuit denoise problem through the root-finding framework proposed by van den Berg and Friedlander (SIAM J Sci Comput 31(2):890–912, 2008). The algorithm is especially well suited to simple domains and could also be used to solve bound-constrained problems as well as problems restricted to the simplex.

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Metadaten
Author:Ewout van den Berg
DOI:https://doi.org/10.1007/s12532-019-00163-5
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2019
Tag:Software; Theoretical Computer Science
Volume:12
Issue:1
Page Number:38
First Page:1
Last Page:38
Mathematical Programming Computation :MPC 2020 - Issue 1
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