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An Implementation of Shor's r-Algorithm

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Abstract

Here we introduce a new implementation of well-known Shor's r-algorithm with space dilations along the difference of two successive (sub)gradients for minimization of a nonlinear (non-smooth) function (N.Z. Shor, Minimization methods for Non-Differentiable Functions, Springer-Verlag: Berlin, 1985. Springer Series in Computational Mathematics, vol. 3). The modifications made to Shor's algorithm are heuristic. They mostly concern the termination criteria and the line search strategy. A large number of test runs indicate that this implementation is very robust, efficient and accurate. We hope that this implementation of Shor's r-algorithm will prove to be useful for solving a wide class of non-smooth optimization problems.

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Authors and Affiliations

  1. Institute for Mathematics, University of Graz, Heirichstr., 36, A-8010, Graz, Austria

    Franz Kappel & Alexei V. Kuntsevich

Authors
  1. Franz Kappel
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  2. Alexei V. Kuntsevich
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Kappel, F., Kuntsevich, A.V. An Implementation of Shor's r-Algorithm. Computational Optimization and Applications 15, 193–205 (2000). https://doi.org/10.1023/A:1008739111712

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  • DOI: https://doi.org/10.1023/A:1008739111712

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