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Journal of Optimization Theory and Applications

, Volume 166, Issue 3, pp 889–905 | Cite as

Diagonal Bundle Method for Nonsmooth Sparse Optimization

  • Napsu Karmitsa
Article

Abstract

We propose an efficient diagonal bundle method for sparse nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions, which are not necessary differentiable or convex. The numerical experiments have been made using problems with up to million variables. The results to be presented confirm the usability of the diagonal bundle method especially for extremely large-scale problems.

Keywords

Nondifferentiable optimization Sparse problems Bundle methods Diagonal variable metric methods 

Mathematics Subject Classification

65K05 90C25 

Notes

Acknowledgments

The work was financially supported by the University of Turku (Finland) and Magnus Ehrnrooth foundation.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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