A Double Accelerated Distributed Algorithm Over Time-Varying Directed Networks for Optimization Problem

摘要

#$%^&*AU2019101520A420200123.pdf#####Abstract In this patent, we focus on solving optimization problems by a group of agents which aim at collaboratively minimizing the sum of all local objective functions over time-varying directed networks, and particularly each of them has only access to its own objective function. In order to solve optimization problems in an effective and efficient way, a double accelerated distributed optimization algorithm based on gradient tracking technique and using uncoordinated step-sizes, is developed. Via incorporating both distributed heavy-ball method and distributed Nesterov method, the algorithm realizes double acceleration. By utilizing both row- and column- stochastic weight matrices, the algorithm can bypass the implementation of double stochastic weight matrices and avoid eigenvector estimation existing in some algorithms using only row- or column- stochastic weight matrices. Thus, the algorithm has the value of practical applications.1/3 Start Each agent sets k=O and sets a stopping criterion Each agent initializes local variables. Compute system parameters Each agent selects a step size and a momentum parameter according to the system parameters Each agent receives/ sends variables from/to its neighbor agents Each agent updates the variables Each agent sets k=k+1 Each agent reets a predefined stopping criterion or not? Y End Figure 1