New distributed optimization algorithm using network node information transfer strategy

This paper is based on the well-known belief propagation theory in statistical learning to study distributed algorithms for nonlinear convex optimization problems. Through in-depth research on the calculation and information transfer process on and between nodes in the network graph of the optimization problem, combined with the belief propagation theory, an information transfer strategy suitable for distributed optimization algorithms is obtained. Under the framework of the centralized classic Newton method and the primal-dual method, the proposed distributed algorithm completes the design using the information transmission in the network. The proposed distributed Newton-Raphson algorithm is a distributed implementation of the centralized Newton method in the case of acyclic connected graphs. The proposed distributed primitive dual algorithm has a similar convergence property of the centralized primal-dual algorithm in the case of acyclic graphs, and it also has better adaptability and robustness for cyclic connected graphs. The simulation experiment illustrates the convergence property and suitable application scenarios of our proposed information transmission strategy and algorithms. © 2021, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.