The Algorithm Research Of Some Distributed Optimization Problems With Special Structure

Multi-agent network composed of multiple agents that have independent work ability is a large-scale network optimization system by the coupling local information.The failure of any agent in the network will not affect the normal operation of the entire network and it has the advantages of saving cost.Therefore,there are diverse applications.For example,distributed model predictive control,network utility maximization,real-time pricing problems for smart grid can be modeled into this class of problems.However,the lack of centralized access network connectivity to information and time changes is a common feature of the multi-agent network structure problem.For this reason,the distributed optimization method associated with multi-agent network should be designed on the basis of local communication,computing and varying network topology.As is known to all,distributed computing allows each agent to have its own cost function and communicate with its immediate neighbors,which potentially has the advantage of protecting the privacy of the agent.In recent years,there is an increasing trend developing distributed optimization by integrating the communication and computation cooperation.The method of solving distributed problem is extensive,such as original consensus distributed algorithm,dual consensus distributed algorithm,primal-dual consensus distributed algorithm and so on.However,in the actual situation,distributed convex optimization problems having constraints and non-convex optimization problems having constraints are of great importance,so it is significant to study the corresponding problems.In this paper,we focus on the related algorithm and convergence results of a class of convex and non-convex optimization problems with separable structures.The rest of this paper is arranged as follows:In the first chapter,we briefly introduce the relevant algorithms and convergence results of distributed optimization problems' research at home and abroad,and give importantly preliminary knowledge.In the second chapter,a convex distributed optimization problem with coupling equality constraints is considered in the time-varying directed graph,and the algorithm and related convergence results are given.More importantly,we show the explicit convergence rate of the algorithm.Finally,numerical examples are given to illustrate that the proposed algorithm is efficient.In the third chapter,we consider a class of strong convex distributed optimization problem with coupling equality constraint under the time-varying directed graph.We propose the algorithm for this problem by introducing the regularized term,and give the relevant convergence results,and show the explicit convergence rate of the algorithm.Finally,numerical simulation proves that the proposed algorithm is effective.In the fourth chapter,considering a class of non-convex distributed optimization problems with convex inequality constraints in the time-varying undirected graph.Combing strong convex approximation,exact penalty function method and consensus mechanism,we propose related algorithm of the problem and relevant convergence results are given.Finally,a numerical example proves that the algorithm is efficient.In the fifth chapter,the author summarizes the research and gives the prospect of the research work.