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A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 8
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Diagonal discrete gradient bundle method for derivative free nonsmooth optimization

Pages 1599-1614 | Received 15 Sep 2015, Accepted 23 Mar 2016, Published online: 07 Apr 2016


Typically, practical nonsmooth optimization problems involve functions with hundreds of variables. Moreover, there are many practical problems where the computation of even one subgradient is either a difficult or an impossible task. In such cases, the usual subgradient-based optimization methods cannot be used. However, the derivative free methods are applicable since they do not use explicit computation of subgradients. In this paper, we propose an efficient diagonal discrete gradient bundle method for derivative-free, possibly nonconvex, nonsmooth minimization. The convergence of the proposed method is proved for semismooth functions, which are not necessarily differentiable or convex. The method is implemented using Fortran 95, and the numerical experiments confirm the usability and efficiency of the method especially in case of large-scale problems.


No potential conflict of interest was reported by the authors.

Additional information


The work was financially supported by the Academy of Finland [Project No. 289500].

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