| With the rapid development of social product, distributed systems has become a hot topic that can analysis and model the complex constituions. Distributed op-timization problem is the main factor in the major enterprise and banks and so on have attracted so many people to research that. In distributed systems, the agents need to change it information with its connected ones, then the communication topology will be changed. But what kind of change ways can make sure the opti-mization result, is what we concerned in this paper. In our works, we have utilize matrix theory and graph theory to completed our research. In our work, the main contributions include:1. Before our work, we have study many current works about distributed optimization, and find that in many result, the topology are always undirected or balanced this make the applying of distributed systems accounted boundedness. what is more, in realistic situation, balance graph is not always satisfied. In view of this, we propose a new algorithms named ratio optimization algorithms, aims to use row Laplace to modle network, and then solove the problem.2. Our work are main about the problem of distributed optimization on direc-tion network. In current work, the multi-agent systems topology are undirected or balanced. After so many research and attmpted work, we show that in any network as long as it is directed, we may take a new approach:auxiliary state-push method, with this way, all the agents can be forced to the same point in the set of optimal solutions. Particularly, our works has extended the applied range existing result, makes distributed realize more worth. In every part, we have do same simulink to prove our result. |
