The speed of Shor's R-algorithm

J. V. Burke, A. S. Lewis, M. L. Overton

Research output: Contribution to journalArticlepeer-review


Shor's r-algorithm is an iterative method for unconstrained optimization, designed for minimizing nonsmooth functions, for which its reported success has been considerable. Although some limited convergence results are known, nothing seems to be known about the algorithm's rate of convergence, even in the smooth case. We study how the method behaves on convex quadratics, proving linear convergence in the two-dimensional case and conjecturing that the algorithm is always linearly convergent, with an asymptotic convergence rate that is independent of the conditioning of the quadratic being minimized.

Original languageEnglish (US)
Pages (from-to)711-720
Number of pages10
JournalIMA Journal of Numerical Analysis
Issue number4
StatePublished - Oct 2008


  • Linear convergence
  • Nonsmooth optimization
  • Shor's r-algorithm
  • Space dilation
  • Unconstrained optimization

ASJC Scopus subject areas

  • General Mathematics
  • Computational Mathematics
  • Applied Mathematics


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