A two-level distributed algorithm for nonconvex constrained optimization
Kaizhao Sun () and
X. Andy Sun ()
Additional contact information
Kaizhao Sun: Georgia Institute of Technology
X. Andy Sun: Massachusetts Institute of Technology
Computational Optimization and Applications, 2023, vol. 84, issue 2, No 11, 609-649
Abstract This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the recent development of distributed algorithms for nonconvex programs, highly complicated constraints still pose a significant challenge in theory and practice. We first identify some difficulties with the existing algorithms based on the alternating direction method of multipliers (ADMM) for dealing with such problems. We then propose a reformulation that enables us to design a two-level algorithm, which embeds a specially structured three-block ADMM at the inner level in an augmented Lagrangian method framework. Furthermore, we prove the global and local convergence as well as iteration complexity of this new scheme for general nonconvex constrained programs, and show that our analysis can be extended to handle more complicated multi-block inner-level problems. Finally, we demonstrate with computation that the new scheme provides convergent and parallelizable algorithms for various nonconvex applications, and is able to complement the performance of the state-of-the-art distributed algorithms in practice by achieving either faster convergence in optimality gap or in feasibility or both.
Keywords: Distributed optimization; Augmented Lagrangian method; Alternating direction method of multipliers; 90C06; 90C26; 90C30; 90C35 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00433-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:84:y:2023:i:2:d:10.1007_s10589-022-00433-4
Ordering information: This journal article can be ordered from
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 ().