A Second Order Primal-Dual Dynamics for Set Constrained Distributed Optimization Problems

The dynamical system with a second-order+first-order structure has been proven to be effective for solving convex optimization problems with equality constraints. In this paper, this structure is extended to distributed optimization to deal with set-constrained convex optimization problems under str...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. II, Express briefs Vol. 71; no. 3; p. 1
Main Authors Tao, Meng, Guo, Luyao, Cao, Jinde, Rutkowski, Leszek
Format Journal Article
LanguageEnglish
Published New York IEEE 01.03.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Constraints
Continuity (mathematics)
Convergence
Convex functions
Convexity
Distributed optimization
Dynamical systems
Heuristic algorithms
Laplace equations
Optimization
primal-dual method
projected dynamics
second-order+first-order structure
Topology
Topology optimization
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Summary:The dynamical system with a second-order+first-order structure has been proven to be effective for solving convex optimization problems with equality constraints. In this paper, this structure is extended to distributed optimization to deal with set-constrained convex optimization problems under strongly connected and weight-balanced directed topology, and a continuous optimization dynamics based on projection operator and primal-dual method is proposed. When proper values of the system parameters are selected, the dynamics converges quickly to the optimal solution of the problem. Finally, two numerical experiments are given to verify the effectiveness of the proposed model.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2023.3324187