Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 59, Issue 8, Pages 3889-3902Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2011.2146776
Keywords
Augmented Lagrangian; convex optimization; distributed algorithm; gossip communication; random networks
Categories
Funding
- Fundacao de Ciencia e Tecnologia (FCT) from Portugal
- FCT [CMU-PT/SIA/0026/2009, SFRH/BD/33518/2008]
- ISR/IST, FEDER
- AFOSR [FA95501010291]
- NSF [CCF1011903]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1011903, 1018509] Funding Source: National Science Foundation
- Fundação para a Ciência e a Tecnologia [SFRH/BD/33518/2008] Funding Source: FCT
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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, decentralized 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: l(1)-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.
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