引用本文:肖丽, 包骏杰, 石熙, 周琳琳.非平衡有向网络上求解分布式经济分配问题的原始-对偶算法[J].西南大学学报(自然科学版),2018,40(11):48~54
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非平衡有向网络上求解分布式经济分配问题的原始-对偶算法
肖丽, 包骏杰, 石熙, 周琳琳1,2
1. 重庆第二师范学院 数学与信息工程学院, 重庆 400065;2. 重庆凯源石油天然气有限责任公司, 重庆 401120
摘要:
受电力系统经济分配问题的启发,研究了分布式经济分配问题,其主要目标是在m个智能体组成的非平衡有向网络上最小化m个局部凸代价函数之和.网络中的每个智能体都仅仅知道自己私有的局部凸代价函数,并且同时受到耦合线性约束和局部不等式约束的影响.此外,特别关注每个智能体仅允许通过不平衡有向网络与其内部邻居进行交互的情况.为了分布式地解决上述问题,提出一种新的只需要智能体进行本地计算和本地通信的完全分布式原始-对偶次梯度算法.当网络拓扑是强连通的且权重矩阵是行随机时,理论分析证明本文的算法可以渐进收敛到全局优化问题的最优解.最后,给出了电力系统中分布式经济分配问题的数值仿真,验证了所提出算法的有效性和分析过程的正确性.
关键词:  非平衡有向网络  经济分配  分布式优化  原始-对偶算法  渐进收敛
DOI:10.13718/j.cnki.xdzk.2018.11.008
分类号:O224
基金项目:重庆市自然科学基金项目(cstc2018jcyjAX0810);重庆市教委科学技术研究项目(KJ1714355,KJ1501408).
A Primal-Dual Algorithm for Solving Distributed Economic Allocation Problem Over a Directed Unbalanced Network
XIAO Li, BAO Jun-jie, SHI Xi, ZHOU Lin-lin1,2
1. Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China;2. ChongqingKaiyuanPetroleum and Natural Gas Company Limited, Chongqing 401120, China
Abstract:
Inspired by the economic allocation problem in power systems, this paper studies the distributed economic allocation problem in power systems where the main goal is to minimize a sum of local convex cost functions over a directed unbalanced network composed of agents. Each agent in the network privately knows its own local convex cost function and is subjected to both coupling linear constraint and individual inequality constraints. Moreover, we particularly focus on the scenario where each agent is only allowed to interact with its in-neighbors over a directed unbalanced network. In order to solve the above problems distributedly, we propose a new fully distributed primal-dual subgradient algorithm that only requires the agent to perform local computing and local communication. Most of the existing algorithms require all agents to possess the out-degree information of their in-neighbors, which is impractical and hardly inevitable as interpreted in the paper. When the network topology is strongly connected and the weight matrix is row stochastic, theoretical analysis proves that our algorithm can converge to the optimal solution of the global optimization problem. Finally, we present a numerical simulation of the distributed economic allocation problem in power systems to verify the effectiveness of the proposed algorithm and the correctness of the analysis process.
Key words:  directed unbalanced network  economic allocation  distributed optimization  primal-dual algorithm  asymptotic convergence
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