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An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions

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Abstract

To construct an effective minimization algorithm for locally Lipschitz functions, we show how to compute a descent direction satisfying Armijo’s condition. We present a finitely terminating algorithm to construct an approximating set for the Goldstein subdifferential leading to the desired descent direction. Using this direction, we propose a minimization algorithm for locally Lipschitz functions and prove its convergence. Finally, we implement our algorithm with matrix laboratory (MATLAB) codes and report our testing results. The comparative numerical results attest to the efficiency of the proposed algorithm.

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Acknowledgements

The first author thanks the Research Council of Sharif University of Technology for supporting this work.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Nezam Mahdavi-Amiri

  2. Department of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Rohollah Yousefpour

Authors
  1. Nezam Mahdavi-Amiri
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  2. Rohollah Yousefpour
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Correspondence to Nezam Mahdavi-Amiri.

Additional information

Communicated by Vladimir F. Dem’yanov.

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Mahdavi-Amiri, N., Yousefpour, R. An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions. J Optim Theory Appl 155, 180–195 (2012). https://doi.org/10.1007/s10957-012-0024-7

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  • DOI: https://doi.org/10.1007/s10957-012-0024-7

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