Douglas–Rachford splitting and ADMM for nonconvex optimization: accelerated and Newton-type linesearch algorithms

Andreas Themelis (), Lorenzo Stella () and Panagiotis Patrinos ()
Additional contact information
Andreas Themelis: Kyushu University
Lorenzo Stella: Amazon
Panagiotis Patrinos: KU Leuven

Computational Optimization and Applications, 2022, vol. 82, issue 2, No 4, 395-440

Abstract: Abstract Although the performance of popular optimization algorithms such as the Douglas–Rachford splitting (DRS) and the ADMM is satisfactory in convex and well-scaled problems, ill conditioning and nonconvexity pose a severe obstacle to their reliable employment. Expanding on recent convergence results for DRS and ADMM applied to nonconvex problems, we propose two linesearch algorithms to enhance and robustify these methods by means of quasi-Newton directions. The proposed algorithms are suited for nonconvex problems, require the same black-box oracle of DRS and ADMM, and maintain their (subsequential) convergence properties. Numerical evidence shows that the employment of L-BFGS in the proposed framework greatly improves convergence of DRS and ADMM, making them robust to ill conditioning. Under regularity and nondegeneracy assumptions at the limit point, superlinear convergence is shown when quasi-Newton Broyden directions are adopted.

Keywords: Nonsmooth nonconvex optimization; Douglas–Rachford splitting; ADMM; Quasi-Newton methods; 90C06; 90C25; 90C26; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00366-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:coopap:v:82:y:2022:i:2:d:10.1007_s10589-022-00366-y

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00366-y

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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