The paper "Distributed Optimization over Time-Varying Directed Graphs" by Angelia Nedić and Alex Olshevsky addresses the problem of distributed convex optimization in a network of nodes, where each node has access to a convex function and the goal is to minimize the sum of these functions. The communication between nodes is described by a time-varying sequence of directed graphs that are uniformly strongly connected. The authors propose a broadcast-based algorithm called subgradient-push, which does not require knowledge of the number of agents or the graph sequence. The subgradient-push algorithm converges to the optimal solution at a rate of \(O(\ln t / \sqrt{t})\), where the constant depends on the initial values, subgradient norms, and the speed of information diffusion and influence imbalances among nodes. The paper provides a detailed analysis of the algorithm's convergence, including a perturbed push-sum protocol and the proof of convergence rates. The results are motivated by applications such as sensor networks and mobile networks, where time-varying directed communications are common.The paper "Distributed Optimization over Time-Varying Directed Graphs" by Angelia Nedić and Alex Olshevsky addresses the problem of distributed convex optimization in a network of nodes, where each node has access to a convex function and the goal is to minimize the sum of these functions. The communication between nodes is described by a time-varying sequence of directed graphs that are uniformly strongly connected. The authors propose a broadcast-based algorithm called subgradient-push, which does not require knowledge of the number of agents or the graph sequence. The subgradient-push algorithm converges to the optimal solution at a rate of \(O(\ln t / \sqrt{t})\), where the constant depends on the initial values, subgradient norms, and the speed of information diffusion and influence imbalances among nodes. The paper provides a detailed analysis of the algorithm's convergence, including a perturbed push-sum protocol and the proof of convergence rates. The results are motivated by applications such as sensor networks and mobile networks, where time-varying directed communications are common.