D4 Published development or research report or study

Double Bundle Method for Nonsmooth DC Optimization




AuthorsKaisa Joki, Adil M. Bagirov, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri

PublisherTurku Centre for Computer Science

Publishing placeTurku

Publication year2017

JournalTUCS Publication Series

Article number1173

Series titleTUCS Technical Report

Number in series1173

ISBN978-952-12-3500-9

ISSN1239-1891

Web address http://tucs.fi/publications/view/?pub_id=tJoBaKaMxTa17a(external)

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/28256928(external)


Abstract

The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth DC optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new stopping procedure guaranteeing Clarke stationarity for solutions by utilizing only DC components of the objective function. This optimality condition is stronger than the criticality condition typically used in DC programming. Moreover, if a candidate solution is not Clarke stationary, then the stopping procedure yields a descent direction. With this new stopping procedure we can avoid some drawbacks, which are encountered when criticality is used. The finite convergence of the method is proved to a Clarke stationary point under mild assumptions. Finally, some encouraging numerical results are presented.


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Last updated on 2024-26-11 at 13:40