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New Proximal Bundle Method for Nonsmooth DC Optimization

Kaisa Joki, Adil M. Bagirov, Napsu Karmitsa, Marko M. Mäkelä, New Proximal Bundle Method for Nonsmooth DC Optimization. TUCS Technical Reports 1130, TUCS, 2015.

Abstract:

In this paper, we develop a version of the bundle method to locally solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to use subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain the so-called nonconvex cutting plane model of the original objective function. We design the proximal bundle method for DC programming based on this approach and prove the convergence of the method to an epsilon-critical point. This algorithm is tested using some academic test problems.

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BibTeX entry:

@TECHREPORT{tJoBaKaMx15a,
  title = {New Proximal Bundle Method for Nonsmooth DC Optimization},
  author = {Joki, Kaisa and Bagirov, Adil M. and Karmitsa, Napsu and Mäkelä, Marko M.},
  number = {1130},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2015},
}

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

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