Discrete gradient method: Derivative-free method for nonsmooth optimization


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Bagirov A. M. , KARASÖZEN B., Sezer M.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol.137, no.2, pp.317-334, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 137 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1007/s10957-007-9335-5
  • Journal Name: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.317-334
  • Keywords: nonsmooth optimization, derivative-free optimization, subdifferentials, discrete gradients, ALGORITHM, SMOOTH

Abstract

A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.