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An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization

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Abstract

In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method.

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Authors and Affiliations

  1. Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, University Drive, Mount Helen, PO Box 663, Ballarat, VIC, 3353, Australia

    Adil Bagirov & Asef Nazari Ganjehlou

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  1. Adil Bagirov
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  2. Asef Nazari Ganjehlou
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Correspondence to Adil Bagirov.

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Bagirov, A., Ganjehlou, A.N. An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization. Math Meth Oper Res 67, 187–206 (2008). https://doi.org/10.1007/s00186-007-0186-5

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  • DOI: https://doi.org/10.1007/s00186-007-0186-5

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