Discrete gradient method: Derivative-free method for nonsmooth optimization

Bagirov, A. M.
Karasözen, Bülent
Sezer, M.
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.


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Tor, Ali Hakan; Karasözen, Bülent; Department of Mathematics (2013)
In this thesis, various numerical methods are developed to solve nonsmooth and in particular, nonconvex optimization problems. More specifically, three numerical algorithms are developed for solving nonsmooth convex optimization problems and one algorithm is proposed to solve nonsmooth nonconvex optimization problems. In general, main differences between algorithms of smooth optimization are in the calculation of search directions, line searches for finding step-sizes and stopping criteria. However, in nonsmoo...
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Karasözen, Bülent (2015-01-01)
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Continuous optimization approaches for clustering via minimum sum of squares
Akteke-Ozturk, Basak; Weber, Gerhard Wilhelm; Kropat, Erik (2008-05-23)
In this paper, we survey the usage of semidefinite programming (SDP), and nonsmooth optimization approaches for solving the minimum sum of squares problem which is of fundamental importance in clustering. We point out that the main clustering idea of support vector clustering (SVC) method could be interpreted as a minimum sum of squares problem and explain the derivation of semidefinite programming and a nonsmooth optimization formulation for the minimum sum of squares problem. We compare the numerical resu...
Citation Formats
A. M. Bagirov, B. Karasözen, and M. Sezer, “Discrete gradient method: Derivative-free method for nonsmooth optimization,” JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, pp. 317–334, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32669.