Max-min eigenvalue problems, primal-dual interior point algorithms, and trust region subproblems

Franz Rendl, Robert J. Vanderbei, Henry Wolkowicz

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and efficient. Both algorithms are based on transforming the problem to one with constraints over the cone of positive semidefinite matrices, i.e. Löwner order constraints. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalOptimization Methods and Software
Volume5
Issue number1
DOIs
StatePublished - Jan 1 1995

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Optimization
  • Applied Mathematics

Keywords

  • 1 programming
  • Graph bisection
  • Löwner partial order
  • Max-min eigenvalue problems
  • Primal-dual interior point methods
  • Quadratic 0
  • Trust region subproblems

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