权重平衡有向网络下分布式约束优化的连续时间算法设计
作者:
中图分类号:

TP18;O224

基金项目:

南京信息工程大学人才启动经费(2020r012);国防科技创新特区项目(2019)


Continuous-time algorithm design for distributed constrained optimization over weight-balanced directed networks
Author:
  • 摘要
  • | |
  • 访问统计
  • |
  • 参考文献
  • |
  • 相似文献
  • | | |
  • 文章评论
    摘要:

    本文研究权重平衡有向网络下分布式约束优化问题的求解,其中网络的全局目标函数是由每个智能体的局部目标函数的和构成,全局的约束是由每个智能体的局部约束的交构成.为了分布式求解该问题的最优解,首先引入智能体的局部共轭函数将其转换为Fenchel对偶问题.其次,从Fenchel对偶问题出发,提出一类基于奇异摄动系统的分布式连续时间算法.在局部目标函数和其梯度分别满足强凸和Lipschitz(李普希兹)连续的情况下,结合凸分析方法和Lyapunov(李雅普诺夫)稳定性理论,结果表明所提算法能够获得原问题和对偶问题的最优值.最后,数值仿真进一步验证了所提算法的有效性.

    Abstract:

    This paper investigates a distributed convex optimization with local constraint sets over weight-balanced directed networks,where the global objective function is described as a sum of some agents' local objective functions.To solve this problem in a distributed way,the problem is transformed into a Fenchel dual problem by introducing local conjugate functions.Then,for the Fenchel dual problem,a distributed continuous-time algorithm is proposed based on the singular perturbation system.When the local objective functions are strongly convex and their gradients are Lipschitz continuous,it is shown that the primal and dual optimality can be both achieved by using the tools from convex analysis and Lyapunov stability.Finally,simulation results are given to illustrate the effectiveness of the proposed algorithm.

    参考文献
    [1] Nedic A,Ozdaglar A.Distributed subgradient methods for multi-agent optimization[J].IEEE Transactions on Automatic Control,2009,54(1):48-61
    [2] Nedic A,Ozdaglar A,Parrilo P A.Constrained consensus and optimization in multi-agent networks[J].IEEE Transactions on Automatic Control,2010,55(4):922-938
    [3] Zhu M H,Martinez S.On distributed convex optimization under inequality and equality constraints[J].IEEE Transactions on Automatic Control,2012,57(1):151-164
    [4] Chang T H,Nedić A,Scaglione A.Distributed constrained optimization by consensus-based primal-dual perturbation method[J].IEEE Transactions on Automatic Control,2014,59(6):1524-1538
    [5] Yuan D M,Ho D W C,Xu S Y.Regularized primal:dual subgradient method for distributed constrained optimization[J].IEEE Transactions on Cybernetics,2016,46(9):2109-2118
    [6] Mateos-Núñez D,Cortés J.Distributed saddle-point subgradient algorithms with laplacian averaging[J].IEEE Transactions on Automatic Control,2017,62(6):2720-2735
    [7] Lee S,Zavlanos M M.Approximate projection methods for decentralized optimization with functional constraints[J].IEEE Transactions on Automatic Control,2018,63(10):3248-3260
    [8] You K Y,Tempo R,Xie P.Distributed algorithms for robust convex optimization via the scenario approach[J].IEEE Transactions on Automatic Control,2019,64(3):880-895
    [9] Lu J,Tang C Y.Zero-gradient-sum algorithms for distributed convex optimization:the continuous-time case[J].IEEE Transactions on Automatic Control,2012,57(9):2348-2354
    [10] Varagnolo D,Zanella F,Cenedese A,et al.Newton-raphson consensus for distributed convex optimization[J].IEEE Transactions on Automatic Control,2016,61(4):994-1009
    [11] Gharesifard B,Cortés J.Distributed continuous-time convex optimization on weight-balanced digraphs[J].IEEE Transactions on Automatic Control,2014,59(3):781-786
    [12] Kia S S,Cortés J,Martínez S.Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication[J].Automatica,2015,55:254-264
    [13] Li Z H,Ding Z T,Sun J Y,et al.Distributed adaptive convex optimization on directed graphs via continuous-time algorithms[J].IEEE Transactions on Automatic Control,2018,63(5):1434-1441
    [14] Zhu Y N,Yu W W,Wen G H,et al.Continuous-time coordination algorithm for distributed convex optimization over weight-unbalanced directed networks[J].IEEE Transactions on Circuits and Systems Ⅱ:Express Briefs,2019,66(7):1202-1206
    [15] Liu Q S,Wang J.A second-order multi-agent network for bound-constrained distributed optimization[J].IEEE Transactions on Automatic Control,2015,60(12):3310-3315
    [16] Zeng X L,Yi P,Hong Y G.Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach[J].IEEE Transactions on Automatic Control,2017,62(10):5227-5233
    [17] Liu Q S,Yang S F,Wang J.A collective neurodynamic approach to distributed constrained optimization[J].IEEE Transactions on Neural Networks and Learning Systems,2017,28(8):1747-1758
    [18] Yang S F,Liu Q S,Wang J.A multi-agent system with a proportional-integral protocol for distributed constrained optimization[J].IEEE Transactions on Automatic Control,2017,62(7):3461-3467
    [19] Zhu Y N,Yu W W,Wen G H,et al.Continuous-time distributed subgradient algorithm for convex optimization with general constraints[J].IEEE Transactions on Automatic Control,2019,64(4):1694-1701
    [20] Zhu Y N,Yu W W,Wen G H,et al.Projected primal:dual dynamics for distributed constrained nonsmooth convex optimization[J].IEEE Transactions on Cybernetics,2020,50(4):1776-1782
    [21] 衣鹏,洪奕光.分布式合作优化及其应用[J].中国科学:数学,2016,46(10):1547-1564 YI Peng,HONG Yiguang.Distributed cooperative optimization and its applications[J].Scientia Sinica (Mathematica),2016,46(10):1547-1564
    [22] 谢佩,游科友,洪奕光,等.网络化分布式凸优化算法研究进展[J].控制理论与应用,2018,35(7):918-927 XIE Pei,YOU Keyou,HONG Yiguang,et al.A survey of distributed convex optimization algorithms over networks[J].Control Theory & Applications,2018,35(7):918-927
    [23] Yang T,Yi X,Wu J,et al.A survey of distributed optimization[J].Annual Reviews in Control,2019,47:278-305
    [24] Wu X Y,Lu J.Fenchel dual gradient methods for distributed convex optimization over time-varying networks[C]//2017 IEEE 56th Annual Conference on Decision and Control (CDC),2017:2894-2899
    [25] Wu X Y,Lu J.Fenchel dual gradient methods for distributed convex optimization over time-varying networks[J].IEEE Transactions on Automatic Control,2019,64(11):4629-4636
    [26] Bertsekas D P.Nonlinear programming[M].Belmont,MA,USA:Athena Scientific,1999
    [27] Ruszczyński A P.Nonlinear optimization[M].Boca Raton,FL:Princeton University Press,2006
    [28] Nesterov Y.Introductory lectures on convex optimization[M].Boston,MA:Springer US,2004
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

朱亚楠,温广辉.权重平衡有向网络下分布式约束优化的连续时间算法设计[J].南京信息工程大学学报(自然科学版),2020,12(5):549-555
ZHU Yanan, WEN Guanghui. Continuous-time algorithm design for distributed constrained optimization over weight-balanced directed networks[J]. Journal of Nanjing University of Information Science & Technology, 2020,12(5):549-555

复制
分享
文章指标
  • 点击次数:337
  • 下载次数: 1885
  • HTML阅读次数: 0
  • 引用次数: 0
历史
  • 收稿日期:2020-07-01
  • 在线发布日期: 2020-10-29

地址:江苏省南京市宁六路219号    邮编:210044

联系电话:025-58731025    E-mail:nxdxb@nuist.edu.cn

南京信息工程大学学报 ® 2025 版权所有  技术支持:北京勤云科技发展有限公司