Distributed Constant-Batch Random Projection Subgradient Algorithm over Switching Balanced Graphs with Time Delays

The distributed constant-batch random projection subgradient algorithm is put forward to solve a constrained non-differentiable convex optimization problem. The constraint set can be written as intersections of some closed convex subsets and each subset is also composed of intersections. The multi-agent network under switching communication graph with fixed time delays is discussed. Each agent only knows its own cost function and is restricted to its own constraint set. A system expansion way is proposed in this paper to convert the network with fixed delays to the network without delays. At each iteration, we randomly select the components of the constant-batch restricted set for each agent and sequentially project the current state of the agent onto the selected sets by using subgradient information. Under the general assumption, the proposed algorithm can make all agents converge to the same optimal point. Finally, we give a numerical simulation example to verify the proposed algorithm.