Discrete gradient method: a derivative free method for nonsmooth optimization

Adil Bagirov (a.bagirovballarat.edu.au)
Bulent Karasozen (bulentmetu.edu.tr)
Meral Sezer (e131029metu.edu.tr)

Abstract: In this paper 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 nonsmooth optimization solver DNLP from CONOPT-GAMS and derivative-free optimization solver CONDOR are presented.

Keywords: nonsmooth optimization, derivative-free optimization, subdifferential, discrete gradients

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: To appear in Journal of Opimization and Applications

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Entry Submitted: 05/01/2006
Entry Accepted: 05/03/2006
Entry Last Modified: 03/24/2007

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