Distributed Synchronous and Asynchronous Algorithms for Semidefinite Programming With Diagonal Constraints

This article develops distributed synchronous and asynchronous algorithms for the large-scale semidefinite programming with diagonal constraints, which has wide applications in combinatorial optimization, image processing, and community detection. The information of the semidefinite programming is a...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 2; pp. 1007 - 1022
Main Authors: Jiang, Xia, Zeng, Xianlin, Sun, Jian, Chen, Jie
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Combinatorial analysis
Communication
Convergence
Costs
Critical point
Distributed algorithms
Distributed optimization
Image processing
Image segmentation
low-rank matrices
Optimization
Programming
Saddle points
Semidefinite programming
semidefinite programming (SDP) with diagonal constraints
Sun
Symmetric matrices
synchronous and asynchronous algorithms
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article develops distributed synchronous and asynchronous algorithms for the large-scale semidefinite programming with diagonal constraints, which has wide applications in combinatorial optimization, image processing, and community detection. The information of the semidefinite programming is allocated to multiple interconnected agents such that each agent aims to find a solution by communicating to its neighbors. Based on the low-rank property of solutions and the Burer-Monteiro factorization, we transform the original problem into a distributed optimization problem over unit spheres to reduce variable dimensions and ensure positive semidefiniteness without involving semidefinite projections, which are computationally expensive. For the distributed optimization problem, we propose distributed synchronous and asynchronous algorithms, both of which reduce computational burden and storage space compared with existing centralized algorithms. Specifically, the distributed synchronous algorithm almost surely escapes strict saddle points and converges to the set of optimal solutions to the optimization problem. In addition, the proposed distributed asynchronous algorithm allows communication delays and converges to critical points to the optimization problem under mild conditions. By applying the proposed algorithms to image segmentation, we illustrate the efficiency and convergence performance of the two proposed algorithms.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3170529