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Continuous-Time Algorithm for Approximate Distributed Optimization With Affine Equality and Convex Inequality Constraints
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DOI：10.1109/TSMC.2019.2957156.png)
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摘要
En 中文
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.
Keyword:
Optimization
Directed graphs
Approximation algorithms
Linear programming
Nickel
Distributed algorithms
Power systems
Constrained distributed optimization
continuous-time algorithm
near-optimal solutions
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期刊
IF:
10.5
论文数:
1.1W
被引数:
5.0W
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