Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

61 Citations (Scopus)


We propose a Newton-CG primal proximal point algorithm (PPA) for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of PPA, the Newton method, and the preconditioned CG solver. When applying the Newton method to solve the inner subproblem, we find that the log-determinant term plays the role of a smoothing term as in the traditional smoothing Newton technique. Focusing on the problem of maximum likelihood sparse estimation of a Gaussian graphical model, we demonstrate that our algorithm performs favorably compared to existing state-of-the-art algorithms and is much preferred when a high quality solution is required for problems with many equality constraints. © 2010 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)2994-3013
Number of pages20
JournalSIAM Journal on Optimization
Issue number6
Publication statusPublished - 1 Dec 2010
Externally publishedYes


  • Log-determinant optimization problem
  • Newton's method
  • Proximal point algorithm
  • Sparse inverse covariance selection

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software


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