An Implementation of Shor's r-Algorithm

  • Authors:
  • Franz Kappel;Alexei V. Kuntsevich

  • Affiliations:
  • Institute for Mathematics, University of Graz, Heirichstr., 36, A-8010 Graz, Austria. franz.kappel@kfunigraz.ac.at;Institute for Mathematics, University of Graz, Heirichstr., 36, A-8010 Graz, Austria. alex@bedvgm.kfunigraz.ac.at

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2000

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Abstract

Here we introduce a new implementation of well-known Shor'sr-algorithm with space dilations along the difference of twosuccessive (sub)gradients for minimization of a nonlinear (non-smooth)function (N.Z. Shor, Minimization methods for Non-DifferentiableFunctions, Springer-Verlag: Berlin, 1985. Springer Seriesin Computational Mathematics, vol. 3).The modifications made to Shor's algorithm areheuristic. They mostly concern the termination criteria and the line searchstrategy. A large number of test runs indicate that this implementationis very robust, efficient and accurate. We hope that this implementationof Shor's r-algorithm will prove to be useful for solvinga wide class of non-smooth optimization problems.