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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 in part by the National Natural Science Foundation of China (62236002, 62403004, 62203001, 62303009, 62136008) and the Open Project of Anhui Key Laboratory of Industrial Energy-Saving and Safety, Anhui University (KFKT202405)
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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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    • References(48)
  • [1]
    J. Huang, J. Wan, B. Lv, Q. Ye, and Y. Chen, “Joint computation offloading and resource allocation for edge-cloud collaboration in internet of vehicles via deep reinforcement learning,” IEEE Syst. J., vol. 17, no. 2, pp. 2500–2511, Jun. 2023. doi: 10.1109/JSYST.2023.3249217
    [2]
    P. K. Saha, N. Chakraborty, A. Mondal, and S. Mondal, “Intelligent real-time utilization of hybrid energy resources for cost optimization in smart microgrids,” IEEE Syst. J., vol. 18, no. 1, pp. 186–197, Mar. 2024. doi: 10.1109/JSYST.2024.3352617
    [3]
    A. N. Sadigh, H. Zayyani, and M. Korki, “A robust proportionate graph recursive least squares algorithm for adaptive graph signal recovery,” IEEE Trans. Circuits Syst. Ⅱ: Express Briefs, vol. 71, no. 7, pp. 3608–3612, Jul. 2024. doi: 10.1109/TCSII.2024.3364090
    [4]
    Z. Chen, J. Wang, and Q.-L. Han, “A collaborative neurodynamic optimization approach to distributed chiller loading,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 8, pp. 10950–10960, Aug. 2024.
    [5]
    Z. Hu, W. Gong, W. Pedrycz, and Y. Li, “Deep reinforcement learning assisted co-evolutionary differential evolution for constrained optimization,” Swarm EComput., vol. 83, p. 101387, Dec. 2023. doi: 10.1016/j.swevo.2023.101387
    [6]
    H.-C. Lu, H.-Y. Tseng, and S.-W. Lin, “Double-track particle swarm optimizer for nonlinear constrained optimization problems,” Inf. Sci., vol. 622, pp. 587–628, Apr. 2023. doi: 10.1016/j.ins.2022.11.164
    [7]
    K. Zhang, X. Zhao, G. Chen, M. Zhao, J. Wang, C. Yao, H. Sun, J. Yao, W. Wang, and G. Zhang, “A double-model differential evolution for constrained waterflooding production optimization,” J. Pet. Sci. Eng., vol. 207, p. 109059, Dec. 2021. doi: 10.1016/j.petrol.2021.109059
    [8]
    C. Liu, S. Ge, and Y. Zhang, “Identifying the cardinality-constrained critical nodes with a hybrid evolutionary algorithm,” Inf. Sci., vol. 642, p. 119140, Sept. 2023.
    [9]
    M. Okulewicz, M. Zaborski, and J. Mańdziuk, “Self-adapting particle swarm optimization for continuous black box optimization,” Appl. Soft Comput., vol. 131, p. 109722, Dec. 2022. doi: 10.1016/j.asoc.2022.109722
    [10]
    Q. Lü, K. Zhang, S. Deng, Y. Li, H. Li, S. Gao, and Y. Chen, “Privacy-preserving decentralized dual averaging for online optimization over directed networks,” IEEE Trans. Ind. Cyber-Phys. Syst., vol. 1, pp. 79–91, 2023.
    [11]
    T. H. Chang, A. Nedić, and A. Scaglione, “Distributed constrained optimization by consensus-based primal-dual perturbation method,” IEEE Trans. Autom. Control, vol. 59, no. 6, pp. 1524–1538, Jun. 2014. doi: 10.1109/TAC.2014.2308612
    [12]
    D. Yuan, D. W. C. Ho, and S. Xu, “Regularized primal-dual subgradient method for distributed constrained optimization,” IEEE Trans. Cybern., vol. 46, no. 9, pp. 2109–2118, Sept. 2016. doi: 10.1109/TCYB.2015.2464255
    [13]
    D. Jakovetić, D. Bajović, J. Xavier, and J. M. F. Moura, “Primal-dual methods for large-scale and distributed convex optimization and data analytics,” Proc. IEEE, vol. 108, no. 11, pp. 1923–1938, Nov. 2020.
    [14]
    S. Han, U. Topcu, and G. J. Pappas, “Differentially private distributed constrained optimization,” IEEE Trans. Autom. Control, vol. 62, no. 1, pp. 50–64, Jan. 2017. doi: 10.1109/TAC.2016.2541298
    [15]
    H. Liu, W. Yu, W. X. Zheng, A. Nedić, and Y. Zhu, “Distributed constrained optimization algorithms with linear convergence rate over time-varying unbalanced graphs,” Automatica, vol. 159, p. 111346, Jan. 2024.
    [16]
    J. Lei, H.-F. Chen, and H.-T. Fang, “Primal-dual algorithm for distributed constrained optimization,” Syst. Control Lett., vol. 96, pp. 110–117, Oct. 2016. doi: 10.1016/j.sysconle.2016.07.009
    [17]
    Q. Liu, S. Yang, and J. Wang, “A collective neurodynamic approach to distributed constrained optimization,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 8, pp. 1747–1758, Aug. 2017. doi: 10.1109/TNNLS.2016.2549566
    [18]
    S. Yang, Q. Liu, and J. Wang, “A multi-agent system with a proportional-integral protocol for distributed constrained optimization,” IEEE Trans. Autom. Control, vol. 62, no. 7, pp. 3461–3467, Jul. 2017. doi: 10.1109/TAC.2016.2610945
    [19]
    Y. Zhu, W. Yu, G. Wen, G. Chen, and W. Ren, “Continuous-time distributed subgradient algorithm for convex optimization with general constraints,” IEEE Trans. Autom. Control, vol. 64, no. 4, pp. 1694–1701, Apr. 2019. doi: 10.1109/TAC.2018.2852602
    [20]
    Y. Zhu, W. Yu, G. Wen, and G. Chen, “Projected primal-dual dynamics for distributed constrained nonsmooth convex optimization,” IEEE Trans. Cybern., vol. 50, no. 4, pp. 1776–1782, Apr. 2020.
    [21]
    X. Li, L. Xie, and Y. Hong, “Distributed continuous-time nonsmooth convex optimization with coupled inequality constraints,” IEEE Trans. Control Netw. Syst., vol. 7, no. 1, pp. 74–84, Mar. 2020. doi: 10.1109/TCNS.2019.2915626
    [22]
    H. Liu, W. X. Zheng, and W. Yu, “Continuous-time algorithm based on finite-time consensus for distributed constrained convex optimization,” IEEE Trans. Autom. Control, vol. 67, no. 5, pp. 2552–2559, May 2022. doi: 10.1109/TAC.2021.3079192
    [23]
    S. Sun, J. Xu, and W. Ren, “Distributed continuous-time algorithms for time-varying constrained convex optimization,” IEEE Trans. Autom. Control, vol. 68, no. 7, pp. 3931–3946, Jul. 2023.
    [24]
    N. Liu, H. Zhang, Y. Chai, and S. Qin, “Two-stage continuous-time triggered algorithms for constrained distributed optimization over directed graphs,” J. Franklin Inst., vol. 360, no. 3, pp. 2159–2181, Feb. 2023.
    [25]
    W. Jia and S. Qin, “An adaptive penalty-like continuous-time algorithm to constrained distributed convex optimization,” J. Franklin Inst., vol. 359, no. 8, pp. 3692–3716, May 2022. doi: 10.1016/j.jfranklin.2022.03.046
    [26]
    T. Yang, X. Yi, J. Wu, Y. Yuan, D. Wu, Z. Meng, Y. Hong, H. Wang, Z. Lin, and K. H. Johansson, “A survey of distributed optimization,” Annu. Rev. Control, vol. 47, pp. 278–305, 2019.
    [27]
    B. Huang, Y. Liu, K. I. Kou, and W. Gui, “Multi-timescale distributed approach to generalized-nash-equilibrium seeking in noncooperative nonconvex games,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 3, pp. 791–793, Mar. 2024. doi: 10.1109/JAS.2023.123909
    [28]
    X. Yi, S. Zhang, T. Yang, T. Chai, and K. H. Johansson, “Communication compression for distributed nonconvex optimization,” IEEE Trans. Autom. Control, vol. 68, no. 9, pp. 5477–5492, Sept. 2023. doi: 10.1109/TAC.2022.3225515
    [29]
    L. Xu, X. Yi, Y. Shi, K. H. Johansson, T. Chai, and T. Yang, “Distributed nonconvex optimization with event-triggered communication,” IEEE Trans. Autom. Control, vol. 69, no. 4, pp. 2745–2752, Apr. 2024. doi: 10.1109/TAC.2023.3339439
    [30]
    X. Liao, Y. Zhao, and X. Zhou, “Neurodynamic flow approach for convex and quasi-convex optimization on Riemannian manifolds with diagonal metrics,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 54, no. 4, pp. 1995–2007, Apr. 2024. doi: 10.1109/TSMC.2023.3329492
    [31]
    R. Xin, U. A. Khan, and S. Kar, “An improved convergence analysis for decentralized online stochastic non-convex optimization,” IEEE Trans. Signal Process., vol. 69, pp. 1842–1858, 2021.
    [32]
    X. Yi, S. Zhang, T. Yang, T. Chai, and K. H. Johansson, “A primal-dual SGD algorithm for distributed nonconvex optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 812–833, May 2022. doi: 10.1109/JAS.2022.105554
    [33]
    J. Zeng and W. Yin, “On nonconvex decentralized gradient descent,” IEEE Trans. Signal Process., vol. 66, no. 11, pp. 2834–2848, Jun. 2018. doi: 10.1109/TSP.2018.2818081
    [34]
    J. Hou, X. Zeng, G. Wang, J. Sun, and J. Chen, “Distributed momentum-based frank-wolfe algorithm for stochastic optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 685–699, Mar. 2023.
    [35]
    B. Houska, J. Frasch, and M. Diehl, “An augmented Lagrangian based algorithm for distributed nonconvex optimization,” SIAM J. Optim., vol. 26, no. 2, pp. 1101–1127, Jan. 2016. doi: 10.1137/140975991
    [36]
    D. Li and X. L. Sun, “Local convexification of the Lagrangian function in nonconvex optimization,” J. Optim. Theory Appl., vol. 104, no. 1, pp. 109–120, Jan. 2000. doi: 10.1023/A:1004628822745
    [37]
    N. Liu, S. Zhao, and S. Qin, “A power reformulation continuous-time algorithm for nonconvex distributed constrained optimization over multi-agent systems,” Neurocomputing, vol. 449, pp. 258–269, Aug. 2021. doi: 10.1016/j.neucom.2021.03.082
    [38]
    Z. Xia, Y. Liu, and J. Wang, “A collaborative neurodynamic approach to distributed global optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 53, no. 5, pp. 3141–3151, May 2023. doi: 10.1109/TSMC.2022.3221937
    [39]
    Z. Xia, W. Yu, Y. Liu, W. Jia, and G. Chen, “Penalty-function-type multi-agent approaches to distributed nonconvex optimal resource allocation,” IEEE Trans. Netw. Sci. Eng., vol. 11, no. 5, pp. 4169–4180, Sept.–Oct. 2024. doi: 10.1109/TNSE.2024.3401748
    [40]
    H. Che and J. Wang, “A collaborative neurodynamic approach to global and combinatorial optimization,” Neural Netw., vol. 114, pp. 15–27, Jun. 2019.
    [41]
    W. Jia, T. Huang, and S. Qin, “A collective neurodynamic penalty approach to nonconvex distributed constrained optimization,” Neural Netw., vol. 171, pp. 145–158, Jun. 2024. doi: 10.1016/j.neunet.2023.12.011
    [42]
    Y. Li, Z. Xia, and Y. Liu, “A p-power neurodynamic approach to distributed nonconvex optimization,” Commun. Nonlinear Sci. Numer. Simul., vol. 134, p. 107999, Jul. 2024. doi: 10.1016/j.cnsns.2024.107999
    [43]
    S. S. Kia, J. Cortés, and S. Martínez, “Dynamic average consensus under limited control authority and privacy requirements,” Int. J. Robust Nonlinear Control, vol. 25, no. 13, pp. 1941–1966, Sept. 2015. doi: 10.1002/rnc.3178
    [44]
    B. Gharesifard and J. Cortes, “Distributed continuous-time convex optimization on weight-balanced digraphs,” IEEE Trans. Autom. Control, vol. 59, no. 3, pp. 781–786, Mar. 2014.
    [45]
    M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms. 3rd ed. Hoboken, USA: John Wiley & Sons, 2013.
    [46]
    H. K. Khalil, Nonlinear Systems. 3rd ed. Upper Saddle River, USA: Prentice-Hall, 2002.
    [47]
    Y. Zhu, W. Yu, G. Wen, and W. Ren, “Continuous-time coordination algorithm for distributed convex optimization over weight-unbalanced directed networks,” IEEE Trans. Circuits Syst. Ⅱ: Express Briefs, vol. 66, no. 7, pp. 1202–1206, Jul. 2019. doi: 10.1109/TCSII.2018.2878250
    [48]
    G. Mancino-Ball, Y. Xu, and J. Chen, “A decentralized primal-dual framework for non-convex smooth consensus optimization,” IEEE Trans. Signal Process., vol. 71, pp. 525–538, 2023.
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