2010/07/31 by Dusan Jakovetic, Dušan Jakovetić, João Xavier +3 · 2 citations
Computer Science · Mathematics · #Algorithm #Augmented Lagrangian method #Computer science #Convex optimization #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #Distributed algorithm #Distributed computing #Gossip #Lagrangian relaxation #Mathematical optimization #Mathematics #Neural Networks Stability and Synchronization #Node (physics) #Optimization problem #Regular polygon #cs.IT #math.IT
paper · pdf · doi:10.1109/tsp.2011.2146776
28 pages, journal; revised
arxiv created 2011/02/06 · openalex publication_date 2011/04/26 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x = x*. The objective function of the corresponding optimization problem is the sum of private (known only by a node), convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, de-centralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping), and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping). The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures), the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.