A partial proximal point algorithm for nuclear norm regularized matrix least squares problems

  • We introduce a partial proximal point algorithm for solving nuclear norm regularized matrix least squares problems with equality and inequality constraints. The inner subproblems, reformulated as a system of semismooth equations, are solved by an inexact smoothing Newton method, which is proved to be quadratically convergent under a constraint non-degeneracy condition, together with the strong semismoothness property of the singular value thresholding operator. Numerical experiments on a variety of problems including those arising from low-rank approximations of transition matrices show that our algorithm is efficient and robust.

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Metadaten
Author:Kaifeng Jiang, Defeng Sun, Kim-Chuan Toh
DOI:https://doi.org/10.1007/s12532-014-0069-8
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2014
Tag:Software; Theoretical Computer Science
Volume:6
Issue:3
Page Number:45
First Page:281
Last Page:325
Mathematical Programming Computation :MPC 2014 - Issue 3
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