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《Journal of Southwest University(Natural Science Edition)》 2018-11
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A Primal-Dual Algorithm for Solving Distributed Economic Allocation Problem Over a Directed Unbalanced Network

XIAO Li;BAO Jun-jie;SHI Xi;ZHOU Lin-lin;Department of Mathematics and Information Engineering,Chongqing University of Education;Chongqing Kaiyuan Petroleum and Natural Gas Company Limited;  
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.
【Fund】: 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)
【CateGory Index】: O224
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