A Partially Inexact Proximal Alternating Direction Method of Multipliers and Its Iteration-Complexity Analysis

Vando A. Adona (), Max L. N. Gonçalves () and Jefferson G. Melo ()
Additional contact information
Vando A. Adona: Universidade Federal de Goiás
Max L. N. Gonçalves: Universidade Federal de Goiás
Jefferson G. Melo: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 10, 640-666

Abstract: Abstract This paper proposes a partially inexact proximal alternating direction method of multipliers for computing approximate solutions of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly using a relative approximate criterion, whereas a proximal term is added to its second subproblem in order to simplify it. A stepsize parameter is included in the updating rule of the Lagrangian multiplier to improve its computational performance. Pointwise and ergodic iteration-complexity bounds for the proposed method are established. To the best of our knowledge, this is the first time that complexity results for an inexact alternating direction method of multipliers with relative error criteria have been analyzed. Some preliminary numerical experiments are reported to illustrate the advantages of the new method.

Keywords: Alternating direction method of multipliers; Relative error criterion; Hybrid extragradient method; Convex program; Pointwise iteration-complexity; Ergodic iteration-complexity; 47H05; 49M27; 90C25; 90C60; 65K10 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01525-8 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:joptap:v:182:y:2019:i:2:d:10.1007_s10957-019-01525-8

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01525-8

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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