Distributed Optimization Algorithms Of Multi-agent Networks Under Complex Communication Conditions

In recent years, with the rapid development of high technology, the coordination and control of multi-agent network has become a hot research issue. Especially the sensors and other small devices,which can be mutually coupled to form a networked system in some way and cooperatively complete a complete task. This distributed coordination control of multi-agent networks have the advantages of low cost, stronger robustness, and therefore can ensure that the equipment can work better under complex conditions. The distributed optimization algorithm of multi-agent network has great advantages in solving the problem of multi-agent coordination and control of multi-agent network. The distributed optimization algorithm of multi-agent network has a great advantage in distributed coordination control of multi-agent network. A multi-agent network contains many agents, where each agent only knows its own objective function and exchange information with other agents to optimize their objective functions, and finally get the optimal solution of the whole network. However, the network may encounter a lot of complex communication conditions during the process of information communications, such as the existence of communication delay or the network is unbalanced network. As a result, the research of distributed optimization algorithms of the multi-agent networks is very significant.In this paper, we mainly study the distributed optimization algorithms of multi-agent network under complex communication conditions, for the complex communication conditions which are easily to appear in the process of information communications such as the presence of communication delay or the communication network is unbalanced network, this paper puts forward the following two kinds of algorithms:Firstly, the distributed randomized gradient-free optimization algorithm with communication delay is studied, where we assume that each agent only knows its own local objective function. The optimization goal is to minimize a sum of local objective functions through the interaction of delay information among agents in the network. Considering the delay of information communication among agents, first we convert the optimization problem with delay into the optimization problem without delay through augmenting delay nodes. Because the local objective function of each agent is likely to be nonconvex, its subgradient does not exist or it is hard to be calculated, we propose the distributed randomized gradient-free method. The theoretical analysis shows that the proposed algorithm is still convergent if the communication delays are upper bounded.Secondly, this paper studies the distributed zero-order Push-sum optimization algorithm of multi-agent network based on the approximate projection. The goal of optimization is to minimize the average value of a sum of local objective functions (possibly non smooth). Because the gradient of each local objective function cannot be accurately calculated, a distributed zero-order method based on the approximate projection is proposed, and the Push-sum algorithm is used for the directed unbalanced communication among agents. The theoretical analysis shows that if the switching network is strongly connected, the proposed algorithm of the network still converges and its convergence rate is O(ln(T+1)/(?)).In summary, this paper proves the distributed random gradient-free optimization algorithm with communication delay is still convergent under the conditions that the communication delays are upper bounded and the directed network is uniformly strongly connected; the proposed distributed zero-order Push-sum optimization algorithm is also convergent under the assumptions that the switching directed network is periodically strongly connected.