An interior-point method for semidefinite programming

Christoph Helmberg, Franz Rendl, Robert J. Vanderbei, Henry Wolkowicz

Research output: Contribution to journalArticlepeer-review

532 Scopus citations


We propose a new interior-point-based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

Original languageEnglish (US)
Pages (from-to)342-361
Number of pages20
JournalSIAM Journal on Optimization
Issue number2
StatePublished - May 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Applied Mathematics


  • Interior-point methods
  • Max-cut relaxations
  • Max-min eigenvalue problems
  • Semidefinite programming


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