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

K. Jiang, Defeng Sun, K.-C. Toh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society. 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 semi-smoothness 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.
Original languageEnglish
Pages (from-to)281-325
Number of pages45
JournalMathematical Programming Computation
Issue number3
Publication statusPublished - 1 Sep 2014
Externally publishedYes


  • 65F10
  • 90C06
  • 90C22
  • 90C25

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

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