Proximal bundle methods for nonsmooth DC programming

Welington Oliveira ()
Additional contact information
Welington Oliveira: CMA – Centre de Mathématiques Appliquées

Journal of Global Optimization, 2019, vol. 75, issue 2, No 10, 523-563

Abstract: Abstract We consider the problem of minimizing the difference of two nonsmooth convex functions over a simple convex set. To deal with this class of nonsmooth and nonconvex optimization problems, we propose new proximal bundle algorithms and show that the given approaches generate subsequences of iterates that converge to critical points. Trial points are obtained by solving strictly convex master programs defined by the sum of a convex cutting-plane model and a freely-chosen Bregman function. In the unconstrained case with the Bregman function being the Euclidean distance, new iterates are solutions of strictly convex quadratic programs of limited sizes. Stronger convergence results (d-stationarity) can be achieved depending on (a) further assumptions on the second DC component of the objective function and (b) solving possibly more than one master program at certain iterations. The given approaches are validated by encouraging numerical results on some academic DC programs.

Keywords: DC programming; Nonsmooth optimization; Bundle methods (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-019-00755-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:75:y:2019:i:2:d:10.1007_s10898-019-00755-4

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-019-00755-4

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().