A1 Journal article – refereed
Double Bundle Method for finding Clarke Stationary Points in Nonsmooth DC Programming

List of Authors: Joki K, Bagirov AM, Karmitsa N, Makela MM, Taheri S
Publication year: 2018
Journal: SIAM Journal on Optimization
Journal name in source: SIAM JOURNAL ON OPTIMIZATION
Journal acronym: SIAM J OPTIMIZ
Volume number: 28
Issue number: 2
Number of pages: 28
ISSN: 1052-6234
eISSN: 1095-7189

The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new escape procedure which enables us to guarantee approximate Clarke stationarity for solutions by utilizing the 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 approximate Clarke stationary, then the escape procedure returns a descent direction. With this escape procedure, we can avoid some shortcomings encountered when criticality is used. The finite termination of the double bundle method to an approximate Clarke stationary point is proved by assuming that the subdifferentials of DC components are polytopes. Finally, some encouraging numerical results are presented.

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Last updated on 2019-21-08 at 22:59