This paper investigates a distributed nonconvex optimization problem constrained by a global coupled linear equality and nonidentical local feasible sets. To solve this problem, we propose a fully distributed alternating direction method of multiplier (ADMM) with a distributed dynamic average consensus for dual variables. Moreover, we demonstrate that the proposed algorithm converges to an approximately stationary solution of the considered problem using Lyapunov theory. Finally, we illustrate the effectiveness of the proposed algorithm by two simulation examples.
AfiaAGougamFRahmouneC, et al. (2024) Intelligent fault classification of air compressors using Harris hawks optimization and machine learning algorithms. Transactions of the Institute of Measurement and Control46(2): 359–378.
2.
AybatNSWangZLinT, et al. (2017) Distributed linearized alternating direction method of multipliers for composite convex consensus optimization. IEEE Transactions on Automatic Control63(1): 5–20.
3.
BaiJHagerWWZhangH (2022) An inexact accelerated stochastic ADMM for separable convex optimization. Computational Optimization and Applications81(2): 479–518.
4.
BiWZhaoLSuiS, et al. (2025) Predefined time output-feedback consensus control for fractional-order nonlinear multi-agent systems. Journal of Systems Science and Complexity38: 2007–2027.
5.
ChangT (2016) A proximal dual consensus ADMM method for multi-agent constrained optimization. IEEE Transactions on Signal Processing64(14): 3719–3734.
6.
ChatzipanagiotisNZavlanosMM (2017) On the convergence of a distributed augmented Lagrangian method for nonconvex optimization. IEEE Transactions on Automatic Control62(9): 4405–4420.
7.
ChengSLiangSFanY, et al. (2023) Distributed gradient tracking for unbalanced optimization with different constraint sets. IEEE Transactions on Automatic Control68(6): 3633–3640.
8.
CongSGuNWangH, et al. (2025) Safety-certified distributed formation control of networked autonomous surface vehicles by unifying control Lyapunov and control barrier functions. Journal of Systems Science and Complexity38(2): 837–856.
9.
FalsoneANotarnicolaINotarstefanoG, et al. (2020) Tracking-ADMM for distributed constraint-coupled optimization. Automatica117: 108962.
10.
FuXPanJWangH, et al. (2020) A formation maintenance and reconstruction method of UAV swarm based on distributed control. Aerospace Science and Technology104: 105981.
11.
HanZLinZFuM (2024) A survey on distributed network localization from a graph Laplacian perspective. Journal of Systems Science and Complexity37(1): 273–293.
12.
HongMLuoZQRazaviyaynM (2016) Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems. SIAM Journal on Optimization26(1): 337–364.
13.
HornRAJohnsonCR (2012) Matrix analysis. Cambridge: Cambridge University Press.
14.
HouJZengXWangG, et al. (2022) Distributed momentum-based Frank-Wolfe algorithm for stochastic optimization. IEEE/CAA Journal of Automatica Sinica10(3): 685–699.
15.
HouskaBFraschJDiehlM (2016) An augmented Lagrangian based algorithm for distributed nonconvex optimization. SIAM Journal on Optimization26(2): 1101–1127.
16.
HuHMoLCaoX (2024) Distributed heterogeneous multi-agent optimization with stochastic sub-gradient. Journal of Systems Science and Complexity37(4): 1470–1487.
17.
HuangQFanYChengS (2024) Distributed unbalanced optimization design over nonidentical constraints. IEEE Transactions on Network Science and Engineering11(4): 3455–3466.
18.
JiangXZengXSunJ, et al. (2022) A fully distributed hybrid control framework for non-differentiable multi-agent optimization. IEEE/CAA Journal of Automatica Sinica9(10): 1792–1800.
19.
LeiJChenH (2019) Distributed stochastic approximation algorithm with expanding truncations. IEEE Transactions on Automatic Control65(2): 664–679.
20.
LiXXieLHongY (2021) Distributed aggregative optimization over multi-agent networks. IEEE Transactions on Automatic Control67(6): 3165–3171.
21.
LiangSYiPHongY (2017) Distributed Nash equilibrium seeking for aggregative games with coupled constraints. Automatica85: 179–185.
22.
LiuYLiuPZhangB (2025) Distributed finite-time optimization for networked Euler-Lagrange systems under a directed graph. Transactions of the Institute of Measurement and Control47(2): 381–389.
23.
LuoJLiuW (2025) Leader-following consensus with prescribed performance for linear multi-agent systems. IEEE Transactions on Automatic Control70(2): 1402–1409.
SunKSunXA (2023) A two-level distributed algorithm for nonconvex constrained optimization. Computational Optimization and Applications84(2): 609–649.
26.
TianJWeiRJiangL (2024) Formation construction and reconfiguration control of UAV swarms: A perspective from distributed assignment and optimization. Nonlinear Dynamics112(23): 21171–21191.
27.
WangLLiuL (2025) A distributed Newton-Raphson extremum seeking algorithm for heterogeneous linear multi-agent systems over unbalanced digraphs. Journal of Systems Science and Complexity38(2): 902–918.
28.
WangYYinWZengJ (2019) Global convergence of ADMM in nonconvex nonsmooth optimization. Journal of Scientific Computing78: 29–63.
29.
WangZLiH (2019) Edge-based stochastic gradient algorithm for distributed optimization. IEEE Transactions on Network Science and Engineering7(3): 1421–1430.
30.
WenGZhengWXWanY (2022) Distributed robust optimization for networked agent systems with unknown nonlinearities. IEEE Transactions on Automatic Control68(9): 5230–5244.
31.
XinJYuLWangJ, et al. (2023) A diversity-based parallel particle swarm optimization for nonconvex economic dispatch problem. Transactions of the Institute of Measurement and Control45(3): 452–465.
32.
YangTYiXWuJ, et al. (2019) A survey of distributed optimization. Annual Reviews in Control47: 278–305.
33.
YangYJiaQXuZ, et al. (2022) Proximal ADMM for nonconvex and nonsmooth optimization. Automatica146: 110551.
34.
YiPHongYLiuF (2016) Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems. Automatica74: 259–269.
35.
YiXZhangSYangT, et al. (2022) A primal-dual SGD algorithm for distributed nonconvex optimization. IEEE/CAA Journal of Automatica Sinica9(5): 812–833.
36.
YuWChengSHeS (2023) Distributed solving linear algebraic equations with switched fractional order dynamics. Journal of Systems Science and Complexity36(2): 613–631.
37.
YuanDHongYHoDW, et al. (2018) Optimal distributed stochastic mirror descent for strongly convex optimization. Automatica90: 196–203.
38.
ZengXYiPHongY, et al. (2018) Distributed continuous-time algorithms for nonsmooth extended monotropic optimization problems. SIAM Journal on Control and Optimization56(6): 3973–3993.
39.
ZhangYLianBLewisFL (2025) Distributed global Nash equilibrium of interactive adversarial graphical games. Journal of Systems Science and Complexity38(2): 613–632.
40.
ZhangYLouYHongY, et al. (2015) Distributed projection-based algorithms for source localization in wireless sensor networks. IEEE Transactions on Wireless Communications14(6): 3131–3142.
41.
ZhiYZhaoZQiM (2023) Event-triggered finite-time consensus control of leader-follower multi-agent systems with unknown velocities. Transactions of the Institute of Measurement and Control45(13): 2515–2525.
