Symmetric primal-dual path-following algorithms for semidefinite programming

Jos F. Sturm, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We propose a framework for developing and analyzing primal-dual interior point algorithms for semidefinite programming. This framework is an extension of the v-space approach that was developed by Kojima et al. (1991) for linear complementarity problems. The extension to semidefinite programming allows us to interpret Nesterov-Todd type directions (Nesterov and Todd 1995, 1997) as Newton search directions. Our approach does not involve any barrier function. Several primal-dual path-following algorithms for semidefinite programming are analyzed. The treatment of these algorithms for semidefinite programming in our setting bears great similarity to the linear programming case.

Original languageEnglish (US)
Pages (from-to)301-315
Number of pages15
JournalApplied Numerical Mathematics
Volume29
Issue number3
DOIs
StatePublished - Mar 1999

Keywords

  • Primal-dual interior point method
  • Primal-dual transformation
  • Semidefinite programming

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