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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  > In Press, Accepted Manuscript
X. Shi and C. Sun, “Penalty function-based distributed primal-dual algorithm for nonconvex optimization problem,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 1–9, Feb. 2025.
Citation: X. Shi and C. Sun, “Penalty function-based distributed primal-dual algorithm for nonconvex optimization problem,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 1–9, Feb. 2025.
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Penalty Function-Based Distributed Primal-Dual Algorithm for Nonconvex Optimization Problem

Funds:  This work was supported by the National Natural Science Foundation of China (62236002, 62403004, 62136008)
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    Abstract
  • This paper addresses the distributed nonconvex optimization problem, where both the global cost function and local inequality constraint function are nonconvex. To tackle this issue, the p-power transformation and penalty function techniques are introduced to reframe the nonconvex optimization problem. This ensures that the Hessian matrix of the augmented Lagrangian function becomes local positive definite by choosing appropriate control parameters. A multi-timescale primal-dual method is then devised based on the Karush-Kuhn-Tucker (KKT) point of the reformulated nonconvex problem to attain convergence. The Lyapunov theory guarantees the model’s stability in the presence of an undirected and connected communication network. Finally, two nonconvex optimization problems are presented to demonstrate the efficacy of the previously developed method.

     

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