Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10107-010-0437-8
DC FieldValue
dc.titleAn implementable proximal point algorithmic framework for nuclear norm minimization
dc.contributor.authorLiu, Y.-J.
dc.contributor.authorSun, D.
dc.contributor.authorToh, K.-C.
dc.date.accessioned2014-10-28T02:30:19Z
dc.date.available2014-10-28T02:30:19Z
dc.date.issued2012-06
dc.identifier.citationLiu, Y.-J., Sun, D., Toh, K.-C. (2012-06). An implementable proximal point algorithmic framework for nuclear norm minimization. Mathematical Programming 133 (1-2) : 399-436. ScholarBank@NUS Repository. https://doi.org/10.1007/s10107-010-0437-8
dc.identifier.issn00255610
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/102836
dc.description.abstractThe nuclear norm minimization problem is to find a matrix with the minimum nuclear norm subject to linear and second order cone constraints. Such a problem often arises from the convex relaxation of a rank minimization problem with noisy data, and arises in many fields of engineering and science. In this paper, we study inexact proximal point algorithms in the primal, dual and primal-dual forms for solving the nuclear norm minimization with linear equality and second order cone constraints. We design efficient implementations of these algorithms and present comprehensive convergence results. In particular, we investigate the performance of our proposed algorithms in which the inner sub-problems are approximately solved by the gradient projection method or the accelerated proximal gradient method. Our numerical results for solving randomly generated matrix completion problems and real matrix completion problems show that our algorithms perform favorably in comparison to several recently proposed state-of-the-art algorithms. Interestingly, our proposed algorithms are connected with other algorithms that have been studied in the literature. © 2011 Springer and Mathematical Optimization Society.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s10107-010-0437-8
dc.sourceScopus
dc.subjectAccelerated proximal gradient method
dc.subjectGradient projection method
dc.subjectNuclear norm minimization
dc.subjectProximal point method
dc.subjectRank minimization
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1007/s10107-010-0437-8
dc.description.sourcetitleMathematical Programming
dc.description.volume133
dc.description.issue1-2
dc.description.page399-436
dc.identifier.isiut000304158900017
Appears in Collections:Staff Publications

Show simple item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

51
checked on Sep 14, 2020

WEB OF SCIENCETM
Citations

50
checked on Sep 14, 2020

Page view(s)

70
checked on Sep 12, 2020

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.