Paper Info
Title
Iteration-complexity analysis of a generalized alternating direction method of multipliers
Abstract
This paper analyzes the iteration-complexity of a generalized alternating direction method of multipliers (G-ADMM) for solving separable linearly constrained convex optimization problems. This ADMM variant, first proposed by Bertsekas and Eckstein, introduces a relaxation parameter \(\alpha \) into the second ADMM subproblem in order to improve its computational performance. It is shown that, for a given tolerance \(\varepsilon >0\), the G-ADMM with \(\alpha \in (0, 2)\) provides, in at most \({\mathcal {O}}(1/\varepsilon ^2)\) iterations, an approximate solution of the Lagrangian system associated to the optimization problem under consideration. It is further demonstrated that, in at most \({\mathcal {O}}(1/\varepsilon )\) iterations, an approximate solution of the Lagrangian system can be obtained by means of an ergodic sequence associated to a sequence generated by the G-ADMM with \(\alpha \in (0, 2]\). Our approach consists of interpreting the G-ADMM as an instance of a hybrid proximal extragradient framework with some special properties. Some preliminary numerical experiments are reported in order to confirm that the use of \(\alpha >1\) can lead to a better numerical performance than \(\alpha =1\) (which corresponds to the standard ADMM).
Year
DOI
Venue
2019
10.1007/s10898-018-0697-z
Journal of Global Optimization
Keywords
Field
DocType
Generalized alternating direction method of multipliers,Hybrid extragradient method,Convex program,Pointwise iteration-complexity,Ergodic iteration-complexity,47H05,49M27,90C25,90C60,65K10
Ergodic sequence,Applied mathematics,Lagrangian system,Mathematical analysis,Separable space,Approximate solution,Optimization problem,Convex optimization,Mathematics
Journal
Volume
Issue
ISSN
73.0
2
1573-2916
Citations 
PageRank 
References 
0
0.34
15
Authors
3
Name
Order
Citations
PageRank
V. A. Adona100.34
M. L. N. Gonçalves2455.93
Jefferson G. Melo3495.63