A sequential semismooth Newton method for the nearest low-rank correlation matrix problem

Qingna Li*, Hou Duo Qi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

Based on the well-known result that the sum of the largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semismooth Newton method, which is shown to be quadratically convergent. The sequential method is guaranteed to produce a stationary point of the nonconvex SDP. Our numerical results demonstrate the high efficiency of the proposed method on large scale problems.

Original languageEnglish
Pages (from-to)1641-1666
Number of pages26
JournalSIAM Journal on Optimization
Volume21
Issue number4
DOIs
Publication statusPublished - 2011
Externally publishedYes

Keywords

  • Constraint nondegeneracy
  • Low-rank correlation matrix
  • Quadratic convergence
  • Quadratic semidefinite programming
  • Semismooth Newton method

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