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A New Subgradient Based Method for Nonsmooth DC Programming

Adil M. Bagirov, Sona Taheri, Kaisa Joki, Napsu Karmitsa, Marko M. Mäkelä, A New Subgradient Based Method for Nonsmooth DC Programming. TUCS Technical Reports 1201, Turku Centre for Computer Science, 2019.

Abstract:

The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers.

BibTeX entry:

@TECHREPORT{tBaTaJoKaMx19a,
  title = {A New Subgradient Based Method for Nonsmooth DC Programming},
  author = {Bagirov, Adil M. and Taheri, Sona and Joki, Kaisa and Karmitsa, Napsu and Mäkelä, Marko M.},
  number = {1201},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2019},
  keywords = {Nonsmooth optimization, Nonconvex optimization, DC optimization, Subgradient method},
  ISBN = {978-952-12-3791-1},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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