| 基于相对状态符号信息的分布式优化算法 |
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| 引用本文： | 张家绮,游科友.基于相对状态符号信息的分布式优化算法[J].南京气象学院学报,2018,10(6):647-657. |
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| 作者姓名： | 张家绮 游科友 |
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| 作者单位： | 清华大学 自动化系, 北京, 100084;清华大学 北京信息科学与技术国家研究中心, 北京, 100084,清华大学 自动化系, 北京, 100084;清华大学 北京信息科学与技术国家研究中心, 北京, 100084 |
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| 基金项目： | 国家自然科学基金（61722308）；国家重点研发计划（2017YFC0805310） |
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| 摘 要： | 针对网络化多智能体的分布式优化问题，本文讨论一种只利用邻居相对状态的符号信息的分布式算法.该算法不要求与图相关的权重矩阵是双随机矩阵.首先利用优化理论中的惩罚函数法解释该算法，然后分析算法在静态图上的收敛性以及收敛速度.与现有使用邻居相对状态的完整信息的分布式梯度下降算法相比，所提算法的收敛速度并没有本质上降低.另一方面，将所提算法扩展到确定性和随机性的时变图上，并给出相应的收敛性结论.最后，通过数值仿真实验验证算法的有效性.
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| 关 键 词： | 分布式优化 多智能体网络 相对状态符号 惩罚函数法 次梯度方法 |
| 收稿时间： | 2018/8/29 0:00:00 |
Distributed optimization using the sign of relative state information |
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| ZHANG Jiaqi and YOU Keyou.Distributed optimization using the sign of relative state information[J].Journal of Nanjing Institute of Meteorology,2018,10(6):647-657. |
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| Authors: | ZHANG Jiaqi and YOU Keyou |
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| Institution: | Department of Automation, Tsinghua University, Beijing 100084;Beijing National Research Centre for Information Science and Technology, Tsinghua Univesity, Beijing 100084 and Department of Automation, Tsinghua University, Beijing 100084;Beijing National Research Centre for Information Science and Technology, Tsinghua Univesity, Beijing 100084 |
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| Abstract: | The design of distributed discrete-time algorithms to cooperatively solve an additive cost optimization problem in multi-agent networks is presented in this paper.The striking feature of the distributed algorithms lies in the use of only the sign of the relative state information between neighbors;which substantially differentiates our algorithms from the existing ones.Moreover,the algorithm does not require the interaction matrix to be doubly stochastic.We first interpret the proposed algorithms in terms of the penalty method in the optimization theory and then perform a non-asymptotic analysis to study the convergence for static network graphs.Compared with the celebrated distributed subgradient algorithms,which,however,use the exact relative state information,the convergence speed in the proposed algorithms is essentially not affected by the loss of information.We also extend our results to the cases of deterministically and randomly time-varying graphs.Finally,we validate the theoretical results through simulations. |
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| Keywords: | distributed optimization multi-agent networks sign of relative state penalty method subgradient iterations |
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