Calibrating least squares semidefinite programming with equality and inequality constraints

Y. Gao, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

45 Citations (Scopus)


In this paper, we consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper, we propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric projection operators. We then design an inexact smoothing Newton method to solve the resulting semismooth system. At each iteration, we use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method. © 2009 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)1432-1457
Number of pages26
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Publication statusPublished - 1 Dec 2009
Externally publishedYes


  • Covariance matrix
  • Quadratic convergence
  • Smoothing Newton method

ASJC Scopus subject areas

  • Analysis

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