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Diagonal discrete gradient bundle method for derivative free nonsmooth optimization
Tekijät: Karmitsa N
Kustantaja: TAYLOR & FRANCIS LTD
Julkaisuvuosi: 2016
Journal: Optimization
Tietokannassa oleva lehden nimi: OPTIMIZATION
Lehden akronyymi: OPTIMIZATION
Vuosikerta: 65
Numero: 8
Aloitussivu: 1599
Lopetussivu: 1614
Sivujen määrä: 16
ISSN: 0233-1934
eISSN: 1029-4945
DOI: https://doi.org/10.1080/02331934.2016.1171865
Tiivistelmä
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.
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.
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