Privacy Preservation of Optimization Algorithm Over Unbalanced Directed Graph

This paper proposes an algorithm with the property of privacy preservation to solve the multi-agent optimization problem, where the communication topology is a fixed and strongly connected directed graph with a row stochastic weight matrix. Here, we consider the external eavesdropper attack model and take the gradient information of the objective function as the agent's privacy information. In this algorithm, each agent adds an additional state variable that interacts with it with a time-varying weight. And this new variable performs gradient iterative calculation. The original state variable interacts with the new variable and the original neighbors. It is proved that the algorithm converges to the optimal solution of the problem and at the same time achieves the purpose of privacy preservation. In addition, the algorithm neither requires additional hidden signals, nor does it increase a large amount of calculation. Finally, a simulation example is given to verify the performance of the algorithm.