A two-level distributed algorithm for nonconvex constrained optimization
Name
10589_2022_Article_433.pdf
Size
3.12 MB
Format
Adobe PDF
Checksum (MD5)
803301435c24731898ec153fa244a07d
Author(s)
Sun, Kaizhao
Sun, X. A.
Date Issued
November 23, 2022
Publisher
Springer US
Citation
Sun, Kaizhao and Sun, X. A. 2022. "A two-level distributed algorithm for nonconvex constrained optimization."
Version
Final published version
Abstract
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.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10589-022-00433-4
