A unified Douglas–Rachford algorithm for generalized DC programming

Chih-Sheng Chuang (), Hongjin He () and Zhiyuan Zhang ()
Additional contact information
Chih-Sheng Chuang: National Chiayi University
Hongjin He: Ningbo University
Zhiyuan Zhang: Xiamen University

Journal of Global Optimization, 2022, vol. 82, issue 2, No 6, 349 pages

Abstract: Abstract We consider a class of generalized DC (difference-of-convex functions) programming, which refers to the problem of minimizing the sum of two convex (possibly nonsmooth) functions minus one smooth convex part. To efficiently exploit the structure of the problem under consideration, in this paper, we shall introduce a unified Douglas–Rachford method in Hilbert space. As an interesting byproduct of the unified framework, we can easily show that our proposed algorithm is able to deal with convex composite optimization models. Due to the nonconvexity of DC programming, we prove that the proposed method is convergent to a critical point of the problem under some assumptions. Finally, we demonstrate numerically that our proposed algorithm performs better than the state-of-the-art DC algorithm and alternating direction method of multipliers (ADMM) for DC regularized sparse recovery problems.

Keywords: Douglas–Rachford algorithm; DC programming; DC algorithm; Alternating direction method of multipliers; Nonconvex optimization (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-021-01079-y 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:82:y:2022:i:2:d:10.1007_s10898-021-01079-y

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

DOI: 10.1007/s10898-021-01079-y

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 ().