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An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization

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  • Adil Bagirov

  • Asef Ganjehlou

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. Copyright Springer-Verlag 2008

Suggested Citation

  • Adil Bagirov & Asef Ganjehlou, 2008. "An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 187-206, April.
    • Handle: RePEc:spr:mathme:v:67:y:2008:i:2:p:187-206
    DOI: 10.1007/s00186-007-0186-5
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    References listed on IDEAS

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    1. E. Polak & J. O. Royset, 2003. "Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 421-457, December.
    2. Bagirov, Adil M. & Yearwood, John, 2006. "A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems," European Journal of Operational Research, Elsevier, vol. 170(2), pages 578-596, April.
    3. A. Bagirov & A. Rubinov & N. Soukhoroukova & J. Yearwood, 2003. "Unsupervised and supervised data classification via nonsmooth and global optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 1-75, June.
    4. A. M. Bagirov & B. Karasözen & M. Sezer, 2008. "Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 317-334, May.
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    Cited by:

    1. A. M. Bagirov & L. Jin & N. Karmitsa & A. Al Nuaimat & N. Sultanova, 2013. "Subgradient Method for Nonconvex Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 416-435, May.
    2. Qu, Shaojian & Liu, Chen & Goh, Mark & Li, Yijun & Ji, Ying, 2014. "Nonsmooth multiobjective programming with quasi-Newton methods," European Journal of Operational Research, Elsevier, vol. 235(3), pages 503-510.

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