Continuous-Time Algorithm for Approximate Distributed Optimization With Affine Equality and Convex Inequality Constraints

A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., t...

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Veröffentlicht in:IEEE transactions on systems, man, and cybernetics. Systems Jg. 51; H. 9; S. 5809 - 5818
Hauptverfasser: Jiang, Xinrui, Qin, Sitian, Xue, Xiaoping
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.09.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximation algorithms
Constrained distributed optimization
Continuity (mathematics)
continuous-time algorithm
Convergence
Critical point
Directed graphs
Distributed algorithms
Linear programming
Load sharing
near-optimal solutions
Nickel
Optimization
Power systems
ISSN:2168-2216, 2168-2232
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Zusammenfassung:A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., the near-optimal solutions of the original DOP) are able to approach the optimal solutions of the original DOP. A continuous-time algorithm is proposed for the ADOP and it is demonstrated that the state solution of the presented algorithm converges to the critical point set of the ADOP with general locally Lipschitz continuous objective functions. This means the presented algorithm is efficient for distributed nonconvex optimization problems. Particularly, when the objective functions are convex ones, the state solution of the presented algorithm is further proved to converge to a near-optimal solution of the original DOP. One illustrative example and an application on load sharing problems are shown to validate the effectiveness of the proposed algorithm.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2019.2957156