This paper presents a novel distributed method for dynamic economic dispatch (DED) problems with cubic fuel cost functions based on the dual alternating direction method of multipliers (D‐ADMM) and interior point method (IPM). This scheme enables us to combine the excellent parallelism of ADMM with the superior convergence properties of the IPM. The idea adopted by the proposed algorithm is that the outer‐loop uses ADMM decoupling, and the inner‐loop uses IPM to solve the cubic polynomial optimization subproblems. When the unit set is divided into multiple partitions, D‐ADMM also has the nice central processing unit (CPU) runtime as the well as the number of iterations. In addition, we use a Decoupling‐Decomposition‐Backtracking and parallel improved multiple centrality corrections decoupling interior point method (DDB‐PIMCCD) to solve the aforementioned larger subproblems more efficiently. Finally, the numerical results, in both serial and parallel modes, on a set of 22 DED cases with the range of units from 8 to 1000 units show that the proposed method is very promising for large scale distributed DED problems. Because it can keep the unit information about each subset in secret to suit the market environment and can obtain high‐quality solutions with reasonable time. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.
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.
more » « less- NSF-PAR ID:
- 10381642
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Computational Optimization and Applications
- Volume:
- 84
- Issue:
- 2
- ISSN:
- 0926-6003
- Page Range / eLocation ID:
- p. 609-649
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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