Distributed subgradient algorithm for multi-agent optimization with directed communication topology

Abstract

This paper studies a distributed subgradient algorithm in directed graphs. In contrast to previous work the problem is considered when the weighted adjacency matrices are not doubly stochastic. First the paper shows that an agreement can be reached in general directed graphs, but the global optimal function may not be minimized. Then some knowledge about homogeneous Markov chains is used to analyze the transition matrices and a new update rule is proposed to ensure that the a lgorithm converges to the optimal set for the case when the topology of graphs is fixed and known to all agents. For switching topology the paper establishes the relationship between the optimal results and the limit vector sequence. The paper provides explicit proof for the results and stimulation research validates the effectiveness.