Distributed subgradient projection algorithm for multi-agent optimization with nonidentical constraints and switching topologies

In this paper, we study a distributed subgradient projection algorithm for multi-agent optimization with nonidentical constraints and switching topologies. We first show that distributed optimization might not be achieved on general strongly connected graphs. Instead, the agents optimize a weighted average of the local objective functions. Then we prove that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the graphs is strongly connected among each time interval of a certain bounded length.