Conditioning of semidefinite programs

Madhu V. Nayakkankuppam, Michael L. Overton

Research output: Contribution to journalArticle

Abstract

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
Volume85
Issue number3
DOIs
StatePublished - 1999

Fingerprint

Semidefinite Program
Conditioning
Strict Complementarity
Explicit Bounds
Nondegeneracy
Primal-dual
Small Perturbations
Linear programming
Quantify
Perturbation
Framework
Complementarity

Keywords

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

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

Cite this

Conditioning of semidefinite programs. / Nayakkankuppam, Madhu V.; Overton, Michael L.

In: Mathematical Programming, Vol. 85, No. 3, 1999, p. 525-540.

Research output: Contribution to journalArticle

Nayakkankuppam, Madhu V. ; Overton, Michael L. / Conditioning of semidefinite programs. In: Mathematical Programming. 1999 ; Vol. 85, No. 3. pp. 525-540.
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