Cooperative convex optimization with subgradient delays using push-sum distributed dual averaging

In this paper, we address the distributed convex optimization problems for multi-agent systems. In our research, it is assumed that each agent in the multi-agent system could merely interact with its neighbors via a directed graph and is available to its own cost function. We then utilize the push-sum distributed dual averaging (PS-DDA) algorithm to tackle with the distributed optimization problem. However, we consider that there exist subgradient delays in PS-DDA algorithm. The proof of the main result which shows that the PS-DDA algorithm with subgradient delays converges and the error possesses sublinear growth of a rate O (tau(2) T-0.5 ), where T denotes the total amount of iterations, is detailed presented in this paper. Finally, a numerical example is simulated to show the performance of the algorithm we study in this paper. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper addresses distributed convex optimization problems for multi-agent systems using the push-sum distributed dual averaging algorithm, while considering subgradient delays. The main result proves that the algorithm converges with sublinear growth of error, and a numerical example is provided to demonstrate its performance.