Conditioning of semidefinite programs

Madhu V. Nayakkankuppam, Michael L. Overton

Research output: Contribution to journalArticlepeer-review


This paper studies the conditioning of semidefinite programs by analyzing the effect of small perturbations in problem data on the solution. Under the assumptions of strict complementarity and non-degeneracy, an explicit bound on the change in the solution is derived in a primal-dual framework, using tools from the Kantorovič theory. This approach also quantifies the size of permissible perturbations. We include a discussion of these results for block diagonal semidefinite programs, of which linear programming is a special case.

Original languageEnglish (US)
Pages (from-to)525-540
Number of pages16
JournalMathematical Programming, Series B
Issue number3
StatePublished - 1999


  • Condition number
  • Kantorovič theory
  • Perturbation theory
  • Semidefinite programming

ASJC Scopus subject areas

  • Software
  • General Mathematics


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